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ROSSMAN Fremont Wayne
Graduate School of Science / Division of Mathematics
Professor

Researcher basic information

■ Degree
  • Ph.D.
■ Research Keyword
  • differential geometry
■ Research Areas
  • Natural sciences / Geometry

Research activity information

■ Paper
  • Discrete Omega-nets and Guichard nets via discrete Koenigs nets
    Francis Burstall, Joseph Cho, Udo Hertrich-Jeromin, Mason Pember, Wayne Rossman
    Jul. 2023, Proceedings London Math. Soc., 126, 790 - 836

  • S. Fujimori, Y. Kawakami, M. Kokubu, W. Rossman, M. Umehara, K. Yamada, S.-D. Yang
    Elsevier BV, Oct. 2022, Differential Geometry and its Applications, 84, 101924 - 101924
    Scientific journal

  • Infinitesimal Darboux transformation and semi-discrete mKdV equation
    Joseph Cho, Wayne Rossman, Tomoya Seno
    2022, Nonlinearity, to appear (NON-104921.R3)

  • Discrete mKdV Equation via Darboux Transformation
    Joseph Cho, Wayne Rossman, Tomoya Seno
    Corresponding, Jul. 2021, Mathematical Physics, Analysis and Geometry, 24(3) (3), article 25 - article 25, English
    [Refereed]
    Scientific journal

  • Discrete minimal nets with symmetries
    Wayne Rossman, Joseph Cho, Seong-Deog Yang
    2021, Springer proceedings, "Minimal surfaces: integrable systems and visualisation", 349, 35 - 50, English
    [Refereed]
    International conference proceedings

  • Analytic extension of exceptional constant mean curvature one catenoids in de Sitter 3-space
    ROSSMAN FREMONT Wayne, FUJIMORI Shoichi, UMEHARA Masaaki, YAMADA Kotaro, KOKUBU Masatoshi, KAWAKAMI Yu
    Jan. 2020, Math. J. Okayama Univ., 62, 179 - 195, English
    [Refereed]
    Scientific journal

  • Discrete Channel Surfaces
    ROSSMAN FREMONT Wayne, Gudrun Szewieczek, Udo Hertrich-Jeromin
    Jan. 2020, Mathematische Zeitschrift, 294(1) (1), 747 - 767, English
    [Refereed]
    Scientific journal

  • Semi-discrete linear Weingarten surfaces with Weierstrass-type representations and their singularities
    ROSSMAN FREMONT Wayne, Masashi Yasumoto
    Jan. 2020, Osaka Journal of Mathematics, 57(1) (1)
    [Refereed]

  • Polynomial Conserved Quantities of Lie Applicable Surfaces
    ROSSMAN FREMONT Wayne, HERTRICH-JEROMIN Udo, BURSTALL Fran, PEMPER Mason
    Feb. 2019, Manuscripta Math., 158(3) (3), 505 - 546, English
    [Refereed]
    Scientific journal
    Link to Kobe Univ. Repository (Kernel)

  • Characterizing singularities of a surface in Lie sphere geometry
    ROSSMAN FREMONT Wayne, PEMBER Mason, SAJI Kentaro, TERAMOTO Keisuke
    2019, Hokkaido Math. J., 48, 281 - 308, English
    [Refereed]
    Scientific journal

  • Discrete linear Weingarten surfaces with singularities in Riemannian and Lorentzian spaceforms
    ROSSMAN FREMONT Wayne, Masashi Yasumoto
    2018, Advanced Studies in Pure Mathematics, 78, 383 - 410, English
    [Refereed]
    Scientific journal

  • Discrete linear Weingarten surfaces
    F. Burstall, U. Hertrich-Jeromin, ROSSMAN FREMONT Wayne
    2018, Nagoya Math. J., 231, 55 - 58, English
    [Refereed]
    Scientific journal

  • Masatoshi Kokubu, Wayne Rossman, Kentaro Saji, Masaaki Umehara, Kotaro Yamada
    University of California, Berkeley, 2018, Pacific Journal of Mathematics, 294(2) (2), 505 - 509, English
    [Refereed]
    Scientific journal

  • Magnetic geodesics on surfaces with singularities
    Volker Branding, ROSSMAN FREMONT Wayne
    Dec. 2017, Pac. J. Math. Ind, 9(3) (3), 29 - 36, English
    [Refereed]
    Scientific journal
    Link to Kobe Univ. Repository (Kernel)

  • ANALYTIC EXTENSION OF JORGE-MEEKS TYPE MAXIMAL SURFACES IN LORENTZ-MINKOWSKI 3-SPACE
    Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara, Kotaro Yamada
    Apr. 2017, OSAKA JOURNAL OF MATHEMATICS, 54(2) (2), 249 - 272, English
    [Refereed]
    Scientific journal

  • Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara, Kotaro Yamada
    Dec. 2016, QUARTERLY JOURNAL OF MATHEMATICS, 67(4) (4), 801 - 837, English
    [Refereed]
    Scientific journal

  • Semi-discrete isothermic surfaces
    F. Burstall, U. Hertrich-Jeromin, C. Mueller, ROSSMAN FREMONT Wayne
    Jul. 2016, Geometriae dedicata, 183, 43 - 58, English
    [Refereed]
    Scientific journal

  • F. Burstall, U. Hertrich-Jeromin, W. Rossman, S. Santos
    Feb. 2015, GEOMETRIAE DEDICATA, 174(1) (1), 1 - 11, English
    [Refereed]
    Scientific journal

  • ZERO MEAN CURVATURE SURFACES IN LORENTZ-MINKOWSKI 3-SPACE WHICH CHANGE TYPE ACROSS A LIGHT-LIKE LINE
    S. Fujimori, Y. W. Kim, S. -E. Koh, W. Rossman, H. Shin, M. Umehara, K. Yamada, S. -D. Yang
    Jan. 2015, OSAKA JOURNAL OF MATHEMATICS, 52(1) (1), 285 - 297, English
    [Refereed]
    Scientific journal

  • Zero mean curvature surfaces in Lorentz-Minkowski 3-space and 2-dimensional fluid mechanics
    Wayne Rossman, FUZIMORI Shoichi, Kim,Young Wook, Koh,Sung-Eun, Shin Heayong, UMEHARA Masaaki, YAMADA Kotaro, Yang,Seong-Deog
    Space-like maximal surfaces and time-like minimal surfacesin Lorentz-Minkowski 3-space R31 are both characterized as zero meancurvature surfaces. We are interested in the case where the zero meancurvature surface changes type from space-like to time-like at a givennon-degenerate null curve. We consider this phenomenon and its interesting connection to 2-dimensional fluid mechanics in this expositoryarticle.
    Department of Mathematics, Faculty of Science, Okayama University, 2015, Mathematical Journal of Okayama University, 57(1) (1), 173 - 200, English
    [Refereed]
    Scientific journal

  • Embedded Triply Periodic Zero Mean Curvature Surfaces of Mixed Type in Lorentz-Minkowski 3-Space
    Shoichi Fujimori, Wayne Rossman, Masaaki Umehara, Kotaro Yamada, Seong-Deog Yang
    2014, MICHIGAN MATHEMATICAL JOURNAL, 63(1) (1), 189 - 207, English
    [Refereed]
    Scientific journal

  • Discrete surfaces of constant mean curvature
    Francis. Burstall E, Hertrich-Jeromin, Wayne Rossman, Santos,S.D
    Kyoto University, 2014, Kokyuroku (RIMS Proceedings), 1880(1880) (1880), 133 - 179, English
    [Refereed]
    International conference proceedings

  • Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara, Kotaro Yamada
    Springer publication, 2013, Springer Proceedings in Mathematics and Statistics, 26, 1 - 47, English
    [Refereed]
    Scientific journal

  • S. Fujimori, Y. W. Kim, S. -E. Koh, W. Rossman, H. Shin, H. Takahashi, M. Umehara, K. Yamada, S. -D. Yang
    Nov. 2012, COMPTES RENDUS MATHEMATIQUE, 350(21-22) (21-22), 975 - 978, English
    [Refereed]
    Scientific journal

  • DISCRETE FLAT SURFACES AND LINEAR WEINGARTEN SURFACES IN HYPERBOLIC 3-SPACE
    T. Hoffmann, W. Rossman, T. Sasaki, M. Yoshida
    Nov. 2012, TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 364(11) (11), 5605 - 5644, English
    [Refereed]
    Scientific journal

  • Weierstrass representation for semi-discrete minimal surfaces, and comparison of various discretized catenoids
    W.~Rossman, M.~Yasumoto
    Oct. 2012, J. Math. for Industry, (Vol. 4 B) (Vol. 4 B), 109 - 118, English
    [Refereed]
    Scientific journal

  • Francis E. Burstall, Udo Hertrich-Jeromin, Wayne Rossman
    Apr. 2012, COMPTES RENDUS MATHEMATIQUE, 350(7-8) (7-8), 413 - 416, English
    [Refereed]
    Scientific journal

  • Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara, Kotaro Yamada
    Oct. 2011, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 87(8) (8), 144 - 149, English
    [Refereed]
    Scientific journal

  • Triviality of the dressing isotropy for a Smyth-type potential and nonclosing of the resulting CMC surfaces
    ROSSMAN Wayne, J. F. Dorfmeister
    May 2011, Iasi conference proceedings, pp. 61-70, English
    [Refereed]
    Scientific journal

  • Corresponding constant mean curvature surfaces in hyperbolic and Euclidean 3-spaces
    ROSSMAN Wayne, M. Toda
    May 2011, Pacific Journal of Applied Mathematics, Vol 3, pp. 37-42, English
    [Refereed]
    Scientific journal

  • THE tt* STRUCTURE OF THE QUANTUM COHOMOLOGY OF CP1 FROM THE VIEWPOINT OF DIFFERENTIAL GEOMETRY
    Josef F. Dorfmeister, Martin A. Guest, Wayne Rossman
    Sep. 2010, ASIAN JOURNAL OF MATHEMATICS, 14(3) (3), 417 - 437, English
    [Refereed]
    Scientific journal

  • Shoichi Fujimori, Wayne Rossman
    Sep. 2010, KYUSHU JOURNAL OF MATHEMATICS, 64(2) (2), 169 - 180, English
    [Refereed]
    Scientific journal

  • Francis E. Burstall, Udo Hertrich-Jeromin, Wayne Rossman
    Jun. 2010, COMPTES RENDUS MATHEMATIQUE, 348(11-12) (11-12), 661 - 664, English
    [Refereed]
    Scientific journal

  • Isothermicity for discrete surfaces in the Euclidean and Minkowski 3-spaces
    ROSSMAN Wayne, Y. Kinoshita
    Mar. 2010, OCAMI Studies, Vol 3, English
    [Refereed]
    Scientific journal

  • David Brander, Wayne Rossman, Nicholas Schmitt
    Feb. 2010, ADVANCES IN MATHEMATICS, 223(3) (3), 949 - 986, English
    [Refereed]
    Scientific journal

  • Discrete minimal catenoid in hyperbolic 3-space
    Udo Hertrich-Jeromin, ROSSMAN FREMONT Wayne
    2010, Electronic Geometry Model, No. 2010.11.001, English
    [Refereed]
    Scientific journal

  • Shoichi Fujimori, Wayne Rossman, Masaaki Umehara, Kotaro Yamada, Seong-Deog Yang
    Dec. 2009, RESULTS IN MATHEMATICS, 56(1-4) (1-4), 41 - 82, English
    [Refereed]
    Scientific journal

  • Asymptotic behavior of flat surfaces in hyperbolic 3-space
    ROSSMAN Wayne, M. Kokubo, M. Umehara, K. Yamada
    Aug. 2009, Journal of The Mathematical Society of Japan, Vol 61, pp. 799-852, English
    [Refereed]
    Scientific journal

  • Spacelike mean curvature one surfaces in de Sitter 3-space
    S. Fujimori, W. Rossman, M. Umehara, K. Yamada, S. -D. Yang
    Jul. 2009, COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 17(3) (3), 383 - 427, English
    [Refereed]
    Scientific journal

  • Period problems for mean curvature one surfaces in H^3 with application to surfaces of low total curvature
    ROSSMAN Wayne, M. Umehara, K. Yamada
    Dec. 2008, Advanced Studies in Pure Math. 51, 2008, Surveys on Geometry and Integrable Systems, Vol 51, pp. 335-387, English
    [Refereed]
    Scientific journal

  • M. Kilian, W. Rossman, N. Schmitt
    Jan. 2008, COMPOSITIO MATHEMATICA, 144(1) (1), 186 - 220, English
    [Refereed]
    Scientific journal

  • Wayne Rossman, Nahid Sultana
    2008, Tokyo Journal of Mathematics, 31(1) (1), 161 - 174, English
    [Refereed]
    Scientific journal

  • David Brander, Wayne Rossman, Nicholas Schmitt
    2008, Journal of Geometry and Symmetry in Physics, 12, 15 - 26, English
    [Refereed]
    International conference proceedings

  • David Brander, Wayne Rossman
    Mathematical Society of the Rep. of China, 2008, Taiwanese Journal of Mathematics, 12(7) (7), 1739 - 1749, English
    [Refereed]
    Scientific journal

  • Conserved quantities in the theory of discrete surfaces
    ROSSMAN Wayne
    Jul. 2007, Proceedings of the "Symposium on the differential geometry of submanifolds", pp. 1-16, English
    [Refereed]
    Scientific journal

  • Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms
    N. Schmitt, M. Kilian, S.-P. Kobayashi, W. Rossman
    Jun. 2007, JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 75, 563 - 581, English
    [Refereed]
    Scientific journal

  • Discrete constant mean curvature surfaces via conserved quantities in any space form
    ROSSMAN Wayne
    May 2007, Progress in Surface Theory, Oberwolfach Report 24, pp. 26-28, English
    [Refereed]
    Scientific journal

  • Morse index of constant mean curvature tori of revolution in the 3-sphere
    ROSSMAN Wayne, Sultana Nahid
    2007, Illinois J. Math., Vol 51. No. 4, pp. 1329-1340, English
    [Refereed]
    Scientific journal

  • Flat fronts in hyperbolic 3-space and their caustics
    Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara, Kotaro Yamada
    Jan. 2007, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 59(1) (1), 265 - 299, English
    [Refereed]
    Scientific journal

  • Simultaneous unitarizability of SLnC-valued maps, and constant mean curvature k-noid monodromy
    Wayne Rossman, Nicholas Schmitt
    2006, ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 5(4) (4), 549 - 577, English
    [Refereed]
    Scientific journal

  • Singularities of flat fronts in hyperbolic space
    M Kokubu, W Rossman, K Saji, M Umehara, K Yamada
    Oct. 2005, PACIFIC JOURNAL OF MATHEMATICS, 221(2) (2), 303 - 351, English
    [Refereed]
    Scientific journal

  • M Kilian, SP Kobayashi, W Rossman, N Schmitt
    Aug. 2005, JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 72, 258 - 272, English
    Scientific journal

  • The first bifurcation point for Delaunay nodoids
    W Rossman
    2005, EXPERIMENTAL MATHEMATICS, 14(3) (3), 331 - 342, English
    Scientific journal

  • Infinite periodic discrete minimal surfaces without self-intersections
    Wayne Rossman
    2005, BALKAN JOURNAL OF GEOMETRY AND ITS APPLICATIONS, 10(2) (2), 106 - 128, English
    Scientific journal

  • Mean Curvature 1 Surfaces in H3 with low total curvature I .
    Wayne Rossman, UMEHARA, Masaaki, YAMADA, Kotaro
    A complete surface of constant mean curvature $1$ (CMC-$1$) inhyperbolic $3$-space with constant curvature $-1$has two natural notions of ``total curvature''---one is the {\em total absolute curvature} which is the integral overthe surface of the absolute value of the Gaussian curvature,and the other is the {\em dual total absolute curvature} which is thetotal absolute curvature of the dual CMC-$1$ surface. In thispaper, we completely classify CMC-$1$ surfaces with dual totalabsolute curvature at most $4\pi$.Moreover, we give new examples and partially classify CMC-$1$surfaces with dual total absolute curvature at most $8\pi$.
    Hiroshima University, 2004, Hiroshima Math. J., 34,21-56(1) (1), 21 - 56, English
    [Refereed]
    Scientific journal

  • Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature II
    W Rossman, M Umehara, K Yamada
    Sep. 2003, TOHOKU MATHEMATICAL JOURNAL, 55(3) (3), 375 - 395, English
    Scientific journal

  • W Rossman
    Sep. 2002, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 34, 599 - 609, English
    [Refereed]
    Scientific journal

  • Discrete constant mean curvature surfaces and their index
    K Polthier, W Rossman
    Aug. 2002, JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 549, 47 - 77, English
    [Refereed]
    Scientific journal

  • P Berard, LL de Lima, W Rossman
    Jan. 2002, MATHEMATISCHE ZEITSCHRIFT, 239(1) (1), 99 - 115, English
    [Refereed]
    Scientific journal

  • Discrete spectrum and Weyl's asymptotic formula for incomplete manifolds
    ROSSMAN FREMONT Wayne, MASAMUNE Jun
    2002, Advanced Studies in Pure Math., 34, 219 - 229, English
    [Refereed]
    Scientific journal

  • Constant mean curvature 1 surfaces with low total curvature in hyperbolic 3-space
    ROSSMAN FREMONT Wayne, UMEHARA Masaki, YAMADA Kotaro
    2002, Advanced Studies in Pure Math., 34, 245 - 253, English
    [Refereed]
    Scientific journal

  • The Morse index of Wente tori
    W Rossman
    Jun. 2001, GEOMETRIAE DEDICATA, 86(1-3) (1-3), 129 - 151, English
    [Refereed]
    Scientific journal

  • Techniques for studying CMC 1 surfaces in hyperbolic three-space
    ROSSMAN FREMONT Wayne
    2001, Tohoku Math. Publ., 20, 153 - 162, English
    [Refereed]
    Scientific journal

  • Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space
    ROSSMAN FREMONT Wayne
    2001, J. Geom. Anal., 11, 669 - 692, English
    [Refereed]
    Scientific journal

  • Mean curvature 1 surfaces in hyperbolic 3-space
    ROSSMAN FREMONT Wayne, UMEHARA Masaaki, YAMADA Kotaro
    2001, EG-Models, 2001.01, 48 - 50, English
    [Refereed]
    Scientific journal

  • Lower bounds for index of Wente tori
    Levi Lopes, de Lima, Vicente Francisco de, Sousa Neto, ROSSMAN FREMONT Wayne
    Hiroshima University, 2001, Hiroshima Math. J, 31(2)(2) (2), 183 - 199, English
    [Refereed]
    Scientific journal

  • On embeddedness of area-minimizing disks, and an application to constructing complete minimal surfaces
    W Rossman
    Jan. 2000, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 52(1) (1), 25 - 40, English
    [Refereed]
    Scientific journal

  • Embedded, doubly periodic minimal surfaces
    W Rossman, EC Thayer, M Wohlgemuth
    2000, EXPERIMENTAL MATHEMATICS, 9(2) (2), 197 - 219, English
    [Refereed]
    Scientific journal

  • Discrete minimal and constant mean curvature surfaces
    ROSSMAN FREMONT Wayne, POLTHIER Konrad
    2000, EG-Models, 2000.01-05-11, 01 - 05-11, English
    [Refereed]
    Scientific journal

  • Flux for mean curvature 1 surfaces in hyperbolic 3-space, and applications
    W Rossman, M Umehara, K Yamada
    Jul. 1999, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 127(7) (7), 2147 - 2154, English
    [Refereed]
    Scientific journal

  • Wente Tori and Morse Index
    ROSSMAN FREMONT Wayne
    1999, An. Acad. Bras. Ci., 71, 607 - 613, English
    [Refereed]
    Scientific journal

  • On the index of constant mean curvature 1 surfaces in hyperbolic space
    Levi Lopes de Lima, ROSSMAN FREMONT Wayne
    1998, Indiana Univ. Math. J., 47(2), 685 - 723, English
    [Refereed]
    Scientific journal

  • Wayne Rossman
    1998, Kyushu Journal of Mathematics, 52(1) (1), 209 - 225, English
    [Refereed]
    Scientific journal

  • Minimal and Constant Mean Curvature Surfaces in R3 and H3
    ROSSMAN FREMONT Wayne
    1998, Proceedings of Workshop in Pure Math., Korean Acad. Council, 17, 161 - 194, English
    [Refereed]
    International conference proceedings

  • Constant mean curvature surfaces with two ends in hyperbolic space
    W Rossman, K Sato
    1998, EXPERIMENTAL MATHEMATICS, 7(2) (2), 101 - 119, English
    [Refereed]
    Scientific journal

  • Irreducible constant mean curvature 1 surfaces in hyperbolic space with positive genus
    W Rossman, M Umehara, K Yamada
    Dec. 1997, TOHOKU MATHEMATICAL JOURNAL, 49(4) (4), 449 - 484, English
    [Refereed]
    Scientific journal

  • Limit Surfaces of Riemann Examples
    ROSSMAN FREMONT Wayne, HOFFMAN David
    1997, J. Geometric Analysis, 7, 161 - 171, English
    [Refereed]
    Scientific journal

  • Minimal surfaces with catenoid ends
    J Berglund, W Rossman
    Dec. 1995, PACIFIC JOURNAL OF MATHEMATICS, 171(2) (2), 353 - 371, English
    [Refereed]
    Scientific journal

  • MINIMAL-SURFACES IN R(3) WITH DIHEDRAL SYMMETRY
    W ROSSMAN
    Mar. 1995, TOHOKU MATHEMATICAL JOURNAL, 47(1) (1), 31 - 54, English
    [Refereed]
    Scientific journal

  • New Examples of Minimal Surfaces
    ROSSMAN FREMONT Wayne
    1993, Research Bulletin, MSJ International Research Institute, Tohoku Univ, -, 369 - 377, English
    [Refereed]
    Scientific journal

■ MISC
  • Discrete surfaces in differential geometry
    Wayne Rossman, Masashi Yasumoto
    2021, Suugaku, 73(1) (1), 1 - 21

  • Discrete Isothermicity in Moebius Subgeometries
    J. Cho, W. Rossman
    2020, Anam Lecture Notes (Ed. S.-D. Yang), 2, 37 - 81

  • On the history of the 4-color mapping problem
    Wayne Rossman, Masashi Yasumoto
    2018, Suugaku Seminar, 9, 43 - 47

  • ZERO MEAN CURVATURE SURFACES IN LORENTZ-MINKOWKI 3-SPACE WHICH CHANGE TYPE ACROSS A LIGHT-LIKE LINE (vol 52, pg 285, 2015)
    S. Fujimori, Y. W. Kim, S. -E. Koh, W. Rossman, H. Shin, M. Umehara, K. Yamada, S. -D. Yang
    Jan. 2016, OSAKA JOURNAL OF MATHEMATICS, 53(1) (1), 289 - 292, English
    Others

  • 離散的な曲面(翻訳：Wayne Rossman）
    近藤 剛史, ROSSMAN FREMONT Wayne
    2010, 数理科学, 48(11), 19 - 25, Japanese
    Report scientific journal

  • Discrete constant mean curvature surfaces via conserved quantities
    ROSSMAN FREMONT Wayne
    2010, MI Lecture Note, 25, English
    Meeting report

  • Computers and Mathematics: Applications of computers to integrable systems methods for constructing constant mean curvature surfaces
    ROSSMAN Wayne
    Jan. 2008, Sugaku, Vol 60. No. 1, pp. 95-103, Japanese
    [Refereed]
    Introduction scientific journal

  • FUJIMORI S, KOBAYASHI S P, ROSSMAN WAYNE
    神戸大学理学部数学科, 2005, Rokko Lectures in Math., vol17, 1 - 118, English
    Introduction scientific journal

  • Constructing Mean Curvature 1 Surfaces in H3 with Irregular Ends. Global Theory of Minimal Surfaces
    ROSSMAN WAYNE, UMEHARA M, YAMADA K
    2005, Proceedings of the Clay Mathematics Institute 2001 Summer School, vol.2, pp 561 584, English
    Introduction scientific journal

  • DISCRETE CONSTANT MEAN CURVATURE SURFACES AND THEIR INDEX (Development in Discrete Integrable Systems : Ultra-Discretization, Quantization)
    Polthier Konrad, Rossman Wayne
    Kyoto University, Jul. 2001, RIMS Kokyuroku, 1221, 125 - 154, English

■ Books And Other Publications
  • Differential Geometry of Curves and Surfaces with Singularities
    Masaaki Umehara, Kentaro Saji, Kotaro Yamada, Translator Wayne Rossman
    translator, World Scientific Publishing Co., 2021

  • Differential Geometry of Curves and Surfaces(翻訳担当Wayne Rossman）
    M. Umehara, K. Yamada, ROSSMAN FREMONT Wayne
    Single translation, World Scientific Publishing Co, 2017, English, ISBN: 9789814740234
    Textbook

  • Rokko Lecture in Mathematics, “Isothermic surfaces in Moebius and Lie sphere geometries”
    ROSSMAN FREMONT Wayne
    Single work, 神戸大学, 2014, English
    Scholarly book

  • Constant mean curvature surfaces (翻訳担当Wayne Rossman日本語題名：可視化の技術と現代幾何学）
    若山正人, ROSSMAN FREMONT Wayne
    Joint work, 岩波書店, 2010, Japanese
    Report

■ Lectures, oral presentations, etc.
  • Broadening discrete surface classes
    Wayne Rossman
    Discrete Geometric Analysis and its Applications, Tohoku University, Jan. 2022, English
    [Invited]

  • Discrete Omega Surfaces
    Wayne Rossman
    Fukuoka University Differential Geometry Meeting 2021, Nov. 2021, Japanese
    [Invited]

  • Discretization of Omega surfaces (3 talks)
    Wayne Rossman
    Discrete Differential Geometry Summer School 2021, Sep. 2021
    [Invited]

  • Darboux Transformations and Discretization of the mKdV Equation
    Wayne Rossman
    JSIAM 2021 meeting, Sep. 2021, Japanese
    [Invited]

  • Discretization of the mKdV equation via transformation theory of curves and surfaces
    Wayne Rossman
    Colloqium, Texas Technical University (USA), Mar. 2021
    [Invited]

  • Infinitesimal Darboux transformation and semi-discrete mKdV equation
    Wayne Rossman
    Differential Geometry Seminar, Univ. of Turin (Italy), Oct. 2020
    [Invited]

  • Darboux Flow and Semi-Discrete mKdV Equation
    Wayne Rossman
    Mathematics for Industry Crest Ed3ge group, Kyushu University, Oct. 2020
    [Invited]

  • Flat fronts in hyperbolic 3-space as Omega surfaces
    Wayne Rossman
    "Geometric Shape Generation" joint Austria-Japan workshop, Tokyo Inst. Tech., Feb. 2020
    [Invited]

  • Global behavior of smooth surfaces with Weierstrass-type representations
    Wayne Rossman
    Integrable systems and symmetry breaking in geometry, Austria, Sep. 2019
    [Invited]

  • Discrete surfaces with topology and/or singularities
    Wayne Rossman
    M:IV-workshop, Leicester, England, Sep. 2019
    [Invited]

  • Global behavior of discrete surfaces
    Wayne Rossman
    9th International Congress on Industrial and Applied Mathematics - ICIAM 2019, Spain, Jul. 2019, English
    [Invited]
    Oral presentation

  • Surfaces in Moebius (and Lie sphere) geometry
    ROSSMAN FREMONT Wayne
    Joint Japan-Korea Workshop on DDG, Jan. 2019, English, Korea University, Seoul, International conference
    [Invited]
    Invited oral presentation

  • Surface discretization and Lie sphere geometry
    ROSSMAN FREMONT Wayne
    SIDE 13 Conference, Nov. 2018, English, Kyushu University, International conference
    [Invited]
    Invited oral presentation

  • Introduction to Lie sphere geometry and applications to surface theory
    ROSSMAN FREMONT Wayne
    Summer School 2018 in Fukuoka, "Geometric shape generation", Sep. 2018, English, Kyushu University, International conference
    [Invited]
    Invited oral presentation

  • Introduction to Lie sphere geometry and applications to surface theory
    ROSSMAN FREMONT Wayne
    Summer School 2018 in Fukuoka, "Geometric shape generation",, Sep. 2018, English, Kyushu University, International conference
    [Invited]
    Invited oral presentation

  • Singularities on discrete omega surfaces
    ROSSMAN FREMONT Wayne
    "Minimal Surfaces: Integrable Systems and Visualization"(m:iv Summer 2018 Workshop), Aug. 2018, English, Technical University Munich, International conference
    [Invited]
    Invited oral presentation

  • Discrete omega surfaces
    ROSSMAN FREMONT Wayne
    Mini-Workshop on Geometry of Surfaces and Related Topics, Aug. 2018, English, Kobe University, International conference
    [Invited]
    Invited oral presentation

  • Discrete Omega surfaces and their singularities
    ROSSMAN FREMONT Wayne
    微分幾何学・微分式系・特異点論の応用, May 2018, Japanese, 広島工業大学広島校舎, Domestic conference
    [Invited]
    Invited oral presentation

  • Singularities of semi-discrete linear Weingarten surfaces
    ROSSMAN FREMONT Wayne
    大阪市立大学微分幾何学セミナー, May 2017, Japanese, 大阪市立大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Using integrable systems techniques to discretize surface theory
    ROSSMAN FREMONT Wayne
    One day Oktoberfest geometry workshop, Oct. 2016, English, Weseda University, International conference
    [Invited]
    Invited oral presentation

  • From discrete surface theory to architecture and back
    ROSSMAN FREMONT Wayne
    Geometry and Material Sciences (GEMS) Workshop, Oct. 2016, English, Okinawa Institute of Science and Technology (OIST), International conference
    [Invited]
    Invited oral presentation

  • Surface discretizations that preserve curvature characteristics
    ROSSMAN FREMONT Wayne
    第 63 回幾何学シンポジウム, Aug. 2016, Japanese, Okayama University, Domestic conference
    [Invited]
    Invited oral presentation

  • Discrete linear Weingarten surfaces: singularities of discrete surfaces
    ROSSMAN FREMONT Wayne
    福岡大学微分幾何研究会, Oct. 2015, English, 福岡大学, Domestic conference
    [Invited]
    Invited oral presentation

  • The mathematics of music
    ROSSMAN FREMONT Wayne
    Kobe Summer School in English 2015, Jul. 2015, English, 神戸大学, Domestic conference
    Invited oral presentation

  • Topology and computer graphics as aids in mathematical surface theory, with applications to architecture
    ROSSMAN FREMONT Wayne
    Kobe Studio Computer Graphics Seminar, Jun. 2015, English, 神戸大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Singularities of discretized linear Weingarten surfaces
    Wayne Rossman
    The 9th OCAMI-KNUHGRG Joint Differential Geometry Workshop on Submanifold Geometry and Lie Theory, Feb. 2015, English, 大阪市立大学, International conference
    [Invited]
    Invited oral presentation

  • Discretization of general linear Weingarten surfaces
    Wayne Rossman
    研究集会「Topics in differential geometry and its discretizations」, Jan. 2015, English, 東北大学（AIMS research center）, International conference
    [Invited]
    Invited oral presentation

  • Topology and computer graphics as aids in mathematical surface theory, with applications to architecture
    Wayne Rossman
    研究集会「トポロジーとコンピューター2014」, Nov. 2014, Japanese, 東京大学大学院数理科学研究科, International conference
    [Invited]
    Invited oral presentation

  • Summer Course in Geometric Aspects of Mathematics
    Wayne Rossman
    The isoperimetric problem and soap films, Jul. 2014, English, 神戸大学, Domestic conference
    Oral presentation

  • Linear Weingarten surfaces, isothermicity, and Lie sphere geometry
    Wayne Rossman
    KU-Leuven workshop on geometry and integrable systems, Jul. 2014, English, Dept of ComputerScience, Leuven University, International conference
    [Invited]
    Invited oral presentation

  • How Einstein saw spheres, The fence of least perimeter about a farm of given size
    Wayne Rossman
    Kobe Summer Lectures in English 2014, Jul. 2014, English, 神戸大学, Domestic conference
    Oral presentation

  • Course on Discrete Differential Geometry
    Rossman Wayne
    研究集会, Mar. 2014, Japanese, 福岡大学, 福岡大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Discrete special isothermic surfaces
    Rossman Wayne
    幾何学セミナー, Jan. 2014, English, ウィーン工科大学, オーストリア, International conference
    [Invited]
    Invited oral presentation

  • Discrete isothermic surfaces with quadratic conserved quantities
    Rossman Wayne
    研究集会「Geometry and Something」, Nov. 2013, Japanese, 福岡大学, 福岡大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Discrete surfaces and their computer graphics
    Rossman Wayne
    幾何学セミナー, Oct. 2013, English, ウィーン工科大学, オーストリア, International conference
    [Invited]
    Invited oral presentation

  • Surfaces that envelop isothermic sphere congruences
    Rossman Wayne
    微分幾何学セミナー, Jul. 2013, Japanese, 福岡大学理学部, 福岡大学理学部, Domestic conference
    [Invited]
    Invited oral presentation

  • Surfaces that envelop isothermic sphere congruences
    Rossman Wayne
    研究集会「部分多様体の微分幾何学の深化」, Jun. 2013, Japanese, 京都大学数理解析研究所, 京都大学数理解析研究所, Domestic conference
    [Invited]
    Invited oral presentation

  • 離散平坦接続による離散曲面の構成
    ROSSMAN Wayne
    数学会の特別講演, Mar. 2013, English, Kyoto University, Domestic conference
    [Invited]
    Invited oral presentation

  • Discrete linear Weingarten surfaces
    ROSSMAN Wayne
    Mini Workshop in Differential Geometry, Mar. 2013, English, Tokyo Institute of Technology, International conference
    [Invited]
    Invited oral presentation

  • Comparison of smooth, discrete and semi-discrete surfaces
    ROSSMAN Wayne
    Math-for-Industry 2012 "Information Recovery and Discovery", Oct. 2012, English, Kyushu University, International conference
    [Invited]
    Invited oral presentation

  • Isothermic, more or less
    ROSSMAN Wayne
    幾何学 Summer Symposium, Aug. 2012, English, Kyushu University, Domestic conference
    [Invited]
    Invited oral presentation

  • Global properties of surfaces, using various Weierstrass representations
    ROSSMAN Wayne
    Bath University geometry seminar, Feb. 2012, English, Bath University, Bath University, International conference
    [Invited]
    Invited oral presentation

  • Discrete linear Weingarten surfaces
    ROSSMAN Wayne
    Workshop on Differential Geometry and Geometric Analysis, Dec. 2011, English, 東北大学, 東北大学, International conference
    [Invited]
    Invited oral presentation

  • Discrete linear Weingarten surfaces
    ROSSMAN Wayne
    談話会, Nov. 2011, Japanese, 東京工業大学, 東京工業大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Differential geometric methods for discretizing surface theory
    ROSSMAN Wayne
    Geometry and Something 2011研究集会, Nov. 2011, Japanese, 福岡大学, 福岡大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Surfaces with Weierstrass representations and Lie sphere geometry
    ROSSMAN Wayne
    Geometry seminar, Feb. 2011, English, King's College London, King's College London, International conference
    [Invited]
    Invited oral presentation

  • Lie sphere geometry and Omega surfaces
    ROSSMAN Wayne
    Bath University Geometry Seminar, Nov. 2010, English, Bath University, Bath University, International conference
    [Invited]
    Invited oral presentation

  • Discrete Surfaces and Lie Sphere Geometry
    ROSSMAN Wayne
    The 6th Geometry Conference for Friendship of China and Japan, Sep. 2010, English, Northwest University, Northwest University, 中国, International conference
    [Invited]
    Invited oral presentation

  • An application of Lie sphere geometry to surface theory in discrete differential geometry
    ROSSMAN Wayne
    Workshop on Hypersurfaces Geometry and Integrable Systems, Aug. 2010, Japanese, 東北大学, 東北大学, Domestic conference
    [Invited]
    Invited oral presentation

  • リー球面幾何学とOmega曲面および曲面の微分幾何学的な離散化
    ROSSMAN Wayne
    東北大学幾何学セミナー, Jun. 2010, Japanese, 東北大学, 東北大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Conserved quantities in surface theory
    ROSSMAN Wayne
    International Conference: "The 2nd TIMS-OCAMI Joint International Workshop on Differential Geometry and Geometric Analysis", Mar. 2010, English, Taida Institute for Mathematical Sciences, National Taiwan University,, Taida Institute for Mathematical Sciences, National Taiwan University,Taipei, Taiwan, International conference
    [Invited]
    Invited oral presentation

  • 離散的な微分幾何学と曲面理論（I)（II)（III)
    ROSSMAN FREMONT Wayne
    第9回ワークショップ「離散可積分系・離散微分幾何学チュートリアル」, Feb. 2010, Japanese, 九州大学産業技術数理研究センター, Domestic conference
    [Invited]
    Invited oral presentation

  • Discrete linear Weingarten surfaces in H3
    ROSSMAN Wayne
    Geometry and something 研究集会, Nov. 2009, Japanese, 福岡大学, 福岡大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Topological behavior of constant mean curvature surfaces
    ROSSMAN Wayne
    Conference: The First KOOK-TAPU Joint Seminar, Aug. 2009, Japanese, 大阪市立大学, 大阪市立大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Discrete isothermic surfaces, and applications to architecture
    ROSSMAN Wayne
    International Conference: "Discrete Differential Geometry Miniworkshop'', Jul. 2009, English, Technical University of Denmark, Technical University of Denmark, Copenhagen, Denmark, International conference
    [Invited]
    Invited oral presentation

  • A (limited) survey on the foundations of discrete differential geometry
    ROSSMAN Wayne
    曲線と曲面の変分問題と関連する話題, Jul. 2009, Japanese, 奈良女子大学, 奈良女子大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Surfaces, DPW, and quantum cohomology
    ROSSMAN Wayne
    Conference: New aspects of surface theory, May 2009, Japanese, 首都大学, 首都大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Basic Training for the DPW Method
    ROSSMAN Wayne
    Seminar: GEOSOCK joint OCU-Handai-Shindai geometry seminar, May 2009, Japanese, 大阪大学, 大阪市立大学, 神戸大学, 梅田, 大阪, Domestic conference
    [Invited]
    Invited oral presentation

  • Discrete linear Weingarten surfaces in hyperbolic 3-space
    ROSSMAN Wayne
    International Conference: Differential Geometry with Mira, Apr. 2009, Japanese, 大阪大学, 大阪大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Discrete flat and linear Weingarten surfaces in hyperbolic 3-space
    ROSSMAN Wayne
    Conference: Fusion of Integrable Systems and Geometry, Apr. 2009, Japanese, 東北大学, 東北大学, Domestic conference
    [Invited]
    Invited oral presentation

  • Discrete Surfaces and Architecture
    ROSSMAN Wayne
    国際研究集会「リーマン面，調和写像と可視化」, Dec. 2008, English, 大阪市立大学, 大阪市立大学, International conference
    [Invited]
    Invited oral presentation

  • Flat surfaces in H^3 and Lie sphere geometry
    ROSSMAN Wayne
    Geometry and Something, Nov. 2008, English, 福岡大学, 福岡大学, International conference
    [Invited]
    Invited oral presentation

  • Visualization and Discretization in Surface Theory
    ROSSMAN Wayne
    九州大学産業技術数理コンソーシアム第0回フォーラム『マス・フォア・インダストリ』, Mar. 2008, Japanese, 九州大学「マス・フォア・インダストリ」GCOE, 第一ホテル東京シーフォート, Domestic conference
    [Invited]
    Invited oral presentation

  • Applications of computer graphics to immersions with special curvature properties
    ROSSMAN Wayne
    Mathematical Aspects of Image Processing and Computer Vision, Nov. 2007, English, 北海道大学, 北海道大学, International conference
    [Invited]
    Invited oral presentation

  • Discrete constant mean curvature surfaces in any space form
    ROSSMAN Wayne
    Symposium on the differential geometry of submanifolds, Jul. 2007, English, Luc Vrancken, Valenciennes, Valenciennes, France, International conference
    [Invited]
    Invited oral presentation

  • Conserved quantities and discrete surfaces
    ROSSMAN Wayne
    Polyhedral Surfaces Seminar, Jul. 2007, English, TU-Berlin大学, TU-Berlin, International conference
    Oral presentation

  • Minimal Surfaces in Nature, as a Geometric Inverse Problem
    ROSSMAN Wayne
    Inverse Problems Workshop 2007, Apr. 2007, English, Okinawa Institute of Science and Technology, Okinawa Institute of Science and Technology, International conference
    [Invited]
    Invited oral presentation

  • Discrete constant mean curvature surfaces via linear conserved quantities in any space form
    ROSSMAN Wayne
    Progress in Surface Theory meeting, Apr. 2007, English, Oberwolfach Institute, Oberwolfach, International conference
    [Invited]
    Invited oral presentation

  • 可積分系による離散的な平均曲率一定曲面
    ROSSMAN FREMONT Wayne
    The First Sapporo-Fukuoka Geometry Seminar, Feb. 2007, Japanese, Hokkaido University, Domestic conference
    [Invited]
    Invited oral presentation

  • H^3の平坦な波面について
    ROSSMAN FREMONT Wayne
    Yuzawa submanifolds meeting, Dec. 2006, Japanese, Domestic conference
    [Invited]
    Invited oral presentation

  • Using monodromy to close constant mean curvature surfaces
    Wayne Rossman
    Tokyo Metropolitan University Geometry Seminar, Oct. 2006, English, 首都大学, International conference
    [Invited]
    Invited oral presentation

  • Using monodromy to close constant mean curvature surfaces
    Wayne Rossman
    TMU Geometry Seminar, Oct. 2006, English, 首都大学, Domestic conference
    Invited oral presentation

  • Methods of Integrable Systems in Geometry
    Wayne Rossman
    Integrable Systems meeting, Durham, Aug. 2006, English, Durham University, International conference
    [Invited]
    Invited oral presentation

  • Unitarizing Loop Group Monodromies
    Wayne Rossman
    Technical University Berlin Geometry Seminar, Feb. 2006, English, Technical University Berlin, International conference
    [Invited]
    Invited oral presentation

  • ３次元双曲型空間におけるflat front およびそのcaustic,
    ROSSMAN WAYNE, UMEHARA M, KOKUBU Masatoshi, YAMADA Kotaro
    日本数学会2005 年秋季総合分科会, Sep. 2005, Japanese, 代数学分科会, 岡山大学, Domestic conference
    Oral presentation

  • 可積分系の方法での平均曲率一定曲面
    ROSSMAN WAYNE
    無限可積分系の幾何学的研究, Aug. 2005, Japanese, RIMS共同研究, 開催場所, Domestic conference
    Invited oral presentation

  • Weierstrass 型表現公式の150 年
    ROSSMAN WAYNE
    超幾何微分方程式の幾何学的構造, Feb. 2005, Japanese, Domestic conference
    Oral presentation

  • CMC surfaces of both trinoidal type and of higher genus in space forms,via Weierstrass-type representation
    ROSSMAN FREMONT Wayne
    "Advances in Surface Theory" meeting, Jan. 2005, English, Kloster Benediktbeuern, Germany, International conference
    [Invited]
    Invited oral presentation

  • 平均曲率一定曲面と可積分系の関係
    ROSSMAN FREMONT Wayne
    danwakai, Jun. 2004, Japanese, Kanazawa Univ, Domestic conference
    [Invited]
    Invited oral presentation

  • Constant mean curvature surfaces in R3 with positive genus
    ROSSMAN FREMONT Wayne
    Granada EDGE conference, Feb. 2004, English, International conference
    [Invited]
    Invited oral presentation

  • Closing constant mean curvature surfaces
    ROSSMAN FREMONT Wayne
    TU-Munich geometry seminar, Feb. 2004, English, International conference
    [Invited]
    Invited oral presentation

  • Application of integrable systems techniques to constant mean curvaturesurfaces
    ROSSMAN FREMONT Wayne
    Univ of Bath colloquium, Feb. 2004, English, International conference
    [Invited]
    Invited oral presentation

■ Affiliated Academic Society
  • 日本数学会

■ Research Themes
  • Global behavior of discrete surfaces via integrability
    Rossman W.F, 佐治 健太郎
    日本学術振興会, 科学研究費助成事業, 基盤研究(C), 神戸大学, 01 Apr. 2023 - 31 Mar. 2028
    The purpose of this research is to develop the connection between complex analytic methods in surface theory with the integrable systems methods in transformation theory, and produce new results with this.
    The former methods involve primarily the use of Weierstrass and DPW type representations to construct surfaces with particular curvature properties, the first example of this being minimal surfaces in Euclidean space, but including many other classes of surfaces in a variety of spaceforms. The latter methods include transformations of surfaces, such as Baecklund and Darboux transformations, together with permutability properties, in a Moebius geometric context.

  • Algebraic Geometry and Integrable Systems -- Moduli theory and Equations of Painleve type
    齋藤 政彦, 山田 泰彦, 岩木 耕平, 望月 拓郎, 吉岡 康太, Rossman W.F, 稲場 道明, 光明 新
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (A), Kobe Gakuin University, 01 Apr. 2022 - 31 Mar. 2027

  • Differential geometrey of singularities and its applications
    梅原 雅顕, 山田 光太郎, Rossman W.F, 佐治 健太郎
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Institute of Science Tokyo, 01 Apr. 2021 - 31 Mar. 2026
    1. 一昨年度に取り組んだ藤森氏・川上氏・國分氏・Rossman氏・山田氏との「実解析写像の像の解析的拡張の不可能性」の判定に大きな進展があり，11月の数理解析研究所の研究集会において研究発表を行った．これに平行して，東工大の山田氏，横浜国大の本田氏との共同研究で，上記の理論が完成したという仮定のもとで，「de Sitter 時空内の平均曲率が１のカテノイド型の空間的曲面」の解析的な拡張後の曲面がすべて，これ以上の解析的拡張を持たないことを示した． 2. 埼玉大学の福井氏，東工大の卒業生である木下氏，中国のDonghe Pei氏とHaiou Yu氏らと，３次元Minkowski時空の一般化されたカスプ辺の研究について，昨年度に取り組めなかった次数が４の場合を研究し，論文にして投稿した． 3. 熊本大学の安藤直也氏との共同研究として，３次元時空の空間的曲面と時間的曲面それぞれについて，与えたれた滑らかな関数のヘッセ行列から誘導される行列の固有ベクトル場が曲率線となる座標系を見いだし，応用として，これらの時空の曲面の臍点の指数に関する新たな知見を論文にまとめ，年度内に国際誌に掲載された． 4. 研究分担者の山田氏・佐治氏との共同研究として昨年度に行った「３次元の定曲率空間のカスプ辺の写像芽」に関する研究の発展として，一般化されたツバメの尾を定義し，これらについても同様の結論を引き出すことに成功した． 5. 昨年度に引き続き，協力者の北川氏・榎本氏と，３次元球面内において「はめ込まれた平坦トーラスの直径予想」に取り組み，最終的な解決に「あと一歩」という状況に到達した．また，指導していた修士学生の高田君と平面三角形の諸心の他の空間形への変形について，筆者の実解析写像の研究の応用という位置づけで共同研究を行い，成果があがりつつある．

  • Differential geometrey of singularities and its applications
    梅原 雅顕, 山田 光太郎, Rossman W.F, 佐治 健太郎
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Tokyo Institute of Technology, 01 Apr. 2021 - 31 Mar. 2026
    １．分担者の山田氏，佐治氏，協力者の本田氏，直川氏との共同研究として，波面について知られるZakalyukinの補題をフロンタル特異点にまで拡張し応用を与えた．特に以前，筆者等が与えたツバメの尾の判定条件の証明が簡明になった．関連して，フロンタルではないが，曲面に現れる主要な特異点である「交叉帽子特異点」についても同様の研究を行い，Zakalyukin 型の定理を証明することに成功した．これらを２つの論文にまとめた． ２．3次元de Sitter空間の平均曲率1の空間的な曲面として，「不動点をもつ１係数等長変換群」で不変な曲面が複数存在し，G-catenoid とよばれる．分担者の山田氏・ラスマン氏，協力者の藤森氏，國分氏，川上氏，Yang氏らと，それらの多くが，非自明な解析的な拡張をもち，２次元Double-Cone manifoldの構造をもつことを示した．さらに，この事実から，拡張後のG-catenoidが，これ以上の解析的拡張をもたないことが示せた．この成果は論文として現在投稿中である． ３．ローレンツ・ミンコフスキー時空における超曲面は，すべての点で誘導計量が退化するとき「光的」であるという．分担者の山田氏，協力者の赤嶺氏，本田氏との共同研究により，光的な超曲面で対応する光的ベクトル場が完備となるものは，ユークリッド空間の超曲面の平行曲面族から構成されるものに限ることを示し，いくつかの重要な応用を与えた．この成果は，論文として現在投稿中である． ４．「三次元球面に，はめ込まれた平坦トーラスの直径が，球面の直径に一致するだろう」という予想に長年，筆者は取り組み成果を積んできたが，協力者の北川氏，榎本氏らと共同研究を行い，１つの新たな知見を得ることができた．これを基に今後も研究を継続していく所存である．

  • Discrete differential geometry, Lie sphere geometry, discrete surfaces theory, surface representations
    Rossman W.F, POLLY DENIS
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for JSPS Fellows, Kobe University, 08 Mar. 2023 - 31 Mar. 2024
    During this fiscal year, Denis Polly used this grant to conduct research in discrete differential geometry. One project is on discrete constant mean curvature 1 surfaces in hyperbolic 3-space, including also myselfand Denis and Udo Hertrich-Jeromin of Vienna Technical University and Andrew Sageman-Furnas of North Carolina State University. Another project is on linear Weingarten surfaces that are also Lie minimal, including also Masaya Hara and Tomohiro Tada of Kobe University, and Joseph Cho of TU-Vienna. Denis also worked with other researchers at other universities in Japan, such as Masashi Yasumoto and Tokushima University, and has potential projects developing as a result. In the first of the two projects, he succeeded in extending the notion of edge-constraint to associated families of discrete constant mean curvature 1 surfaces in hyperbolic 3-space. This is significant because up until now the notion of edge-constraint has been applied only to surfaces in Euclidean 3-space. In the second project, it has been shown that any minimal or constant mean curvature or affine linear Weingarten surfaces in Euclidean 3-space that is also Lie minimal must be a surface of revolution, and that the situation is slightly more complicated in the case of surfaces in a non-Euclidean spaceform.

  • Development of analysis and discretization in differential geometry
    Rossman W.F, 安本 真士
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Kobe University, Apr. 2020 - Mar. 2024
    Our purpose: 1) use transformation theory to discretize equations and surfaces in the smooth category, while preserving underlying structures; 2) consider behavior of surfaces within integrable systems having singularities and signature changes. An example of transformation theory giving insight into discretization is isothermic surfaces, with their Darboux transforms. By Bianchi permutability, a mesh of Darboux transforms produces a discrete isothermic surface, elucidating these surfaces' definition. With similar concepts, jointly with J. Cho and T. Seno, we have produced discretization of the potential mKdV equation. Further, jointly with Japanese researchers (see below), singularities, signature changes and analytic extendability of various catenoids in de Sitter 3-space were studied.

  • 齋藤 政彦
    科学研究費補助金／基盤研究(S), Apr. 2017 - Mar. 2022
    Competitive research funding

  • 齋藤 政彦
    科学研究費補助金／基盤研究(A), Apr. 2017 - Mar. 2022
    Competitive research funding

  • Rossman W.F
    学術研究助成基金助成金／基盤研究(C), Apr. 2015 - Mar. 2020
    Competitive research funding

  • Rossman W.F
    特別研究員奨励費, Apr. 2017 - Mar. 2019
    Competitive research funding

  • ROSSMAN W.F
    特別研究員奨励費, Apr. 2015 - Mar. 2018
    Competitive research funding

  • Geometry of curves, surfaces and hypersurfaces with singularities
    UMEHARA Masaaki, YAMADA Kotaro, OHNITA Yoshihiro, MASHIMO Katsuya, HASHIMOTO Hideya, ROSSMAN Wayne, KOISO Norihito, GOTO Ryushi, KOKUBU Masatoshi, FUJIMORI Syoichi, SAJI Kentaro, MIYAOKA Reiko, IZUMIYA Shyuichi, ISHIKAWA Goo, KAWAKAMI Yu, AGAOKA Yoshio, KITAGAWA Yoshihisa, MABUCHI Toshiki
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (A), 01 Apr. 2010 - 31 Mar. 2015
    Using the concept of coherent tangent bundles, we (the head investigator and the research group) found four new Gauss-Bonnet type formulas for closed surfaces with singularities in Euclidean 3-space. Using the fact that a spacelike maximal surface with fold singularities has an analytic extension across those singularities, we showed that the analytic extensions of the triply-periodic Schwarz D type maximal surfaces are all embedded. In a joint work with Yoshihisa Kitagawa, we proved that the Clifford torus is rigid in the class of immersed flat tori whose mean curvature functions do not change sign. Moreover, we obtained some interesting results for plane curves. For example, a simplification of the proof of Bol's conjecture on sextactic points was discovered.

  • Weierstrass-type representation formulas and their application to surfaces with singularities
    YAMADA Kotaro, UMEHARA Masaaki, WAYNE Rossman, YOSHIDA Masaaki, KUROSE Takashi, KOKUBU Masatoshi, FUJIMORI Shoichi, KAWAKAMI Yu, HONDA Atsufumi
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Tokyo Institute of Technology, 01 Apr. 2009 - 31 Mar. 2014
    We investigated, Weierstrass-type representation formula, global properties of several classes of surfaces with singularities, such as flat surfaces in hyperbolic 3-space, maximal surfaces in Minkowski 3-space, CMC-1 surfaces in de Sitter 3-space, and improper affine sphere in affine 3-space, and obtained a charctreization of completeness, Osserman-type inequalis etc. In addition, flat trinoids in hyperbolic space and CMC-1 2-noids in de Sitter 3-space are classified. On the other hand, as a basic tool of differential geometry of wave front, we introduced a notion of "sinular curvature" and investigated a rdelationship between singular curvature and behavior of Gaussian curvature. As a result, we obtained Gauss-Bonnet type formula for wave fronts. Moreover, as an intrinsic formulation of wave fronts, we introduced a notion of "coherent tangent bundles" and gave an application of their duality.

  • Geometry of curves and surfaces with singularities
    UMEHARA Masaaki, YAMADA Kotaro, HASHIMOTO Hideya, MASHIMO Katsuya, MABUCHI Toshiki, KOISO Norihito, GOTO Ryushi, ENOKI Ichiro, W.F. Rossman, MIYAOKA Reiko, KOKUBU Masatoshi, FUJIMORI Shoichi, AGAOKA Yoshio
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (A), Osaka University, 2007 - 2010
    This research was focused on the geometry of curves and surfaces with singularities. We gave a useful criterion for A_k singular points on hypersurfaces, and applied it to the study of inflection points on hypersurfaces. This riterion enabled us to define A_k singularities of wave front without assuming the existence of an ambient space. In fact, we defined the notion "coherent tangent bundle", giving an intrinsic formulation for wave fronts and several other applications. Moreover, we investigated maximal surfaces in Lorentz-Minkowski space and constant mean curvature surfaces in de Sitter space, and constructed several interesting new examples with singularities but still having certain kind of completeness. Additionally, the head investigator and coinvestigators held several workshops (both domestic and international), which related in many fruitful discussions with geometers studying relating fields.

  • Differential geometric researches on surfaces in a space of constant curvature and their singularities
    KOKUBU Masatoshi, IRIE Hiroshi, KOBAYASHI Shimpei, ROSSMAN Wayne
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Tokyo Denki University, 2006 - 2009
    We studied surfaces in a three-dimensional manifold of constant negative curvature, called the hyperbolic space, requiring them to have good properties from the differential-geometric viewpoint. (Note that the hyperbolic space has interesting features beyond our common sense, e.g., a single hyperbolic line has infinitely many parallels.) We clarified the asymptotic behavior of ends of flat surfaces admitting singularities. Concerning linear Weingarten surfaces, we had a global representation formula, criterion for the shape of singularities, the orientability and co-orientability, and so on.

  • W.F Rossman
    科学研究費補助金／萌芽研究, 2008
    Competitive research funding

  • 高山 信毅
    科学研究費補助金／基盤研究(A), 2008
    Competitive research funding

  • W.F Rossman
    科学研究費補助金／基盤研究(B), 2008
    Competitive research funding

  • The global behavior of curves and surfaces in space forms
    UMEHARA Masaaki, KOISO Norihito, YAMADA Kotaro, ROSSMAN Wayne F, KOKUBU Masatoshi, INOGUCHI Junichi
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Osaka University, 2003 - 2006
    We get the following results : 1.A maximal surface which is given by the real part of holomorphic isotropic immersion into C^3 is called a maxface. As a joint work with K.Yamada, the head investigator Umehara gave a Weierstrass-type representation formula for maxfaces, and gave an Osserman-type ineqality for complete maxfaces. The equality holds if and only if all ends of the surfaces are properly embedded. Moreover, as a joint work with K.Saji, S.Fujimori, and K.Yamada, the head investigator Umehara gave a criterion for the cuspidal cross cap, and showed that generic singular points for maxfaces consists of cuspidal edge, swallowtail and cuspidal cross cap. 2.As a joint work with K.Saji and K.Yamada, the head investigator Umehara studied the behavior of Gaussian curvature near the cuspidal edge and the swallowtail. In particular, the new geometric invariant on cuspidal edges called the singular curvature is introduced, and show that the integration of the singular curvature on the singular set is closely related to the Euler number of the surface. 3.A curve γ in the real projective plane is called anti-convex if for each point p on the curve, there exists a line passing through the point which does not meet y other than p. As a joint work with G.Thorbergsson, the head investigator Umehara studied the inflection points on anti-convex curves, and showed that the number of inflection points I and the number of the independent double tangents D satisfies the relation I-2D=3.

  • W.F Rossman
    特別研究員奨励費, 2006
    Competitive research funding

  • ROSSMAN WAYNE, FREMONT
    科学研究費補助金／基盤研究(B), 2005
    Competitive research funding

  • 佐々木 武
    科学研究費補助金／基盤研究(C), 2005
    Competitive research funding

  • Research on surfaces of constant mean curvature one in hyperbolic space and its application
    UMEHARA Masaaki, WAYNE Rossman, YAMADA Kotaro, MATSUMOTO Takao, INOGUCHI Junichi, KOKUBU Masatoshi
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), HIROSHIMA UNIVERSITY, 2001 - 2002
    We get the following results: 1. The head investigator Masaaki Umehara proved that the equality of the Osserman inequality for minimal surfaces in Euclidean n-space holds if and only if each end has no self-intersection and asymptotic to a catenoid or a plane, which is a joint work with M. Kokubu and K. Yamada. Moreover, we construct a new example which attains the equality. 2. The head investigator Masaaki Umehara gave countable many new irreducible constant mean curvature one (i.e. CMC-1) surfaces in hyperbolic 3-space whose ends all irregular, which is a joint work with W. Rossman and K. Yamada. 3. The head investigator Masaaki Umehara gave an elementary proof of the Small's representation formula for CMC-1 surfaces in hyperbolic 3-space and also got a similar representation formula for flat surfaces in hyperbolic 3-space, which is a joint work M. Kokubu and K. Yamada. A flat surface in hyperbolic 3-space called a flat front if it admits singularity but can be lifted to a Legendrian immersion into the unit cotangent bundle of hyperbolic 3-space. We showed flat fronts with complete ends satisfy an Osserman-type inequality with respect to the degree of the hyperbolic Gauss maps. The equality holds if and only if all ends have no self intersection. Furthermore, we classify flat front of genus zero with embedded regular 3-ends and also construct an example of genus one with five regular embedded ends.

  • Construction of submanifold with constant mean curvature, and its applications
    YAMADA Kotaro, ROSSMAN Wayne, CHO Koji, YAMAGUCHI Takao, INOUE Hisao, KUROSE Takashi
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B)., 1998 - 2000
    We investigated properties of minimal surfaces in the three dimensional euclidean space using the Weierstrass representation formula, and generalizations of them. First, we gave an affirmative result for an inverse problem of flux for minimal surfaces in the three dimensional euclidean space. Moreover, as a generalization of (a complex analytic) flux, we defined a new homology invariant, which is also called as "flux", for surfaces of constant mean curvature one in the hyperbolic three space. Using the balancing formula of the flux, we proved some non-existence results for constant mean curvature one surface in hyperbolic space. As a continuation of this non-existence results, we tried to classify the complete constant mean curvature one surface in hyperbolic space with low total absolute curvature, and we obtained the complete classification for surfaces with total absolute curvature less than or equal to 4π. On the other hand, as a generalization of the Weierstrass-type representation formula for minimal surface with higher dimensional euclidean space, we defined a notion of surfaces with holomorphic right gauss map in some non-compact type symmetric space, and obtained the Weierstrass-Bryant type representation formula. As an application of this formula, we obtained an Osserman-type inequality for total absolute curvature.

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