プレプリント

  • Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara and Kotaro Yamada,
    Analytic extension of exceptional constant mean curvature one elliptic catenoids in de Sitter 3-space,

出版予定

  • Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara and Kotaro Yamada
    Analytic extension of Jorge-Meeks type maximal surfaces in Lorentz-Minkowski 3-space ,
    preprint, arXiv:1509.05853 (19 Sept. 2015) , to appear in Osaka Journal of Mathematics.

出版済論文

  • Atsufumi Honda, Miyuki Koiso, Masatoshi Kokubu, Masaaki Umehara and Kotaro Yamada
    Mixed type surfaces with bounded mean curvature in 3-dimensional space-times,
    Differential Geometry and Its Applications, vol. 52 (2017), 64--77.
    http://dx.doi.org/10.1016/j.difgeo.2017.03.009
  • Kentaro Saji, Masaaki Umehara and Kotaro Yamada
    An index formula for hypersurfaces which admit only generic corank one singularities
    Jurnal of Mathematical Society of Japan, vol. 69 No. 1 (2017) 417--457.
    doi: 10.2969/jmsj/06910417
  • Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara and Kotaro Yamada
    Entire zero mean curvature graphs of mixed type in Lorentz-Minkowski 3-space
    The Quaterly Journal of Mathematics, doi:10.1093/qmath/haw038
  • Kosuke Naokawa, Masaaki Umehara and Kotaro Yamada
    Isometric deformations of cuspidal edges
    Tohoku Mathematical Journal (2), vol. 68, Number 1 (2016), 73--90.
    https://projecteuclid.org/euclid.tmj/1458248863
  • Luciana F. Martins, Kentaro Saji, Masaaki Umehara and Kotaro Yamada
    Behavior of Gaussian curvature near non-degenerate singular points on wave fronts
    in "Geometry and Topology of Manifolds", A. Futaki et. al. ed., pages 247--281, Springer Proceedings in Mathematics & Statistics, volume 154, 2016.
    DOI 10.1007/978-4-431-56021-0_14
  • Masaru Hasegawa, Atsufumi Honda, Kosuke Naokawa, Kentaro Saji, Masaaki Umehara and Kotaro Yamada
    Intrinsic properties of surfaces with singularities
    International Journal of Mathematics, Vol. 26, No. 4 (2015) 1540008 (34 pages),
    DOI: 10.1142/S0129167X1540008X.
  • Shoichi Fujimori, Young Wook Kim, Sung-Eun Koh, Wayne Rossman, Heayong Shin, Masaaki Umehara, Kotaro Yamada, Seong-Deog Yang
    Zero mean curvature surfaces in Lorentz-Minkowki 3-space which change type across a light-like line
    Osaka Journal of Mathematics, volue 52 (2015), 285--297.
    http://projecteuclid.org/euclid.ojm/1427202882
    Erratum to the article "Zero mean curvature surfaces in Lorentz-Minkowki 3-space which change type across a light-like line"
    Osaka Journal of Mathematics, volue 53 (2016), 289--293.
  • Shoichi Fujimori, Young Wook Kim, Sung-Eun Koh, Wayne Rossman, Heayong Shin, Masaaki Umehara, Kotaro Yamada, Seong-Deog Yang
    Zero mean curvature surfaces in Lorentz-Minkowski 3-space and 2-dimensional fluid mechanics
  • Udo Hertrich-Jeromin, Yoshihiko Suyama, Masaaki Umehara and Kotaro Yamada
    A duality for conformally flat hypersurfaces
    Beiträge zur Algebra und Geometrie/ Contribution to Algebra and Geometry, 2014, DOI 10.1007/s13366-014-0225-3.
  • Shoichi Fujimori, Wayne Rossman, Masaaki Umehara, Kotaro Yamada, Seong-Deog Yang
    Embedded triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-space
    Michigan Mathematical Journal, volume 63, 2014, 189--207.
  • Masaru Hasegawa, Atsufumi Honda, Kosuke Naokawa, Masaaki Umehara and Kotaro Yamada
    Intrinsic invariants of cross caps
    Selecta Mathematica, volume 20, Issue 3 (2014), 769--785
  • Francisco Martín, Masaaki Umehara and Kotaro Yamada,
    Flat surfaces in hyperbolic 3-space whose hyperbolic Gauss maps are bounded
    Revista Matemática Iberoamericana, 30 (2014), 309--316.
  • Leonor Ferrer, Francisco Martín, Masaaki Umehara and Kotaro Yamada,
    A construction of a complete bounded null curve in C3
    Kodai Mathematical Journal, 37 (2014), 59--96.
  • Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara and Kotaro Yamada
    Hyperbolic metrics on Riemann surfaces and space-like CMC-1 Surfaces in de Sitter 3-Space
    in "Recent Trends in Lorentzian Geometry", M. Sánchez et al. (eds.), Springer Proceedings in Mathematics & Statistics 26, pages 1--47, 2013.
  • Shoichi Fujimori, Young Wook Kim, Sung-Eun Koh, Wayne Rossman, Heayong Shin, Hidenobu Takahashi, Masaaki Umehara, Kotaro Yamada, Seong-Deog Yang
    Zero mean curvature surfaces in L3 containing a light-like line
  • Kentaro Saji, Masaaki Umehara and Kotaro Yamada,
    Coherent tangent bundles and Gauss-Bonnet formulas for wave fronts
  • Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara and Kotaro Yamada,
    CMC-1 trinoids in H3 and metrics of constant curvature one with conical singularities on S2,
    Proceedings of Japan Academy, vol. 87, Ser. A (2011), 144--149.
  • Kentaro Saji, Masaaki Umehara and Kotaro Yamada,
    A2-singularities of hypersurfaces with non-negative sectional curvature in Euclidean space
  • Masaaki Umehara and Kotaro Yamada,
    Applications of a completeness lemma in minimal surface theory to various classes of surfaces
    Bulletin of the London Mathematical Society, vol. 43 (2011), 191--199.
    Corrigendum: Applications of a completeness lemma in minimal surface theory to various classes of surfaces
    Bulletin of the London Mathematical Society, vol. 44 (2012), 617--618.
  • Huili Liu, Masaaki Umehara and Kotaro Yamada,
    The duality of conformally flat manifolds
    Bulletin of the Brasilian Mathematical Society (N. S.), vol. 42 (2011), 131--152.
  • Kentaro Saji, Masaaki Umehara and Kotaro Yamada,
    The duality between singular points and inflection points on wave fronts,
  • Kentaro Saji, Masaaki Umehara and Kotaro Yamada,
    Singularities of Blaschke normal maps of convex surfaces
  • Shoichi Fujimori, Wayne Rossman, Masaaki Umehara, Kotaro Yamada and Seog-Deong Yang,
    New maximal surfaces in Minkowski 3-space with arbitrary genus and their cousins in de Sitter 3-space
  • Shoichi Fujimori, Wayne Rossman, Masaaki Umehara, Kotaro Yamada and Seog-Deong Yang,
    Spacelike mean curvature one surfaces in de Sitter 3-space,
  • Francisco Martín, Masaaki Umehara and Kotaro Yamada,
    Complete bounded holomorphic curves immersed in C2 with arbitrary genus,
  • Francisco Martín, Masaaki Umehara and Kotaro Yamada,
    Complete bounded null curves immersed in C3 and SL(2,C),
    Erratum to: Complete bounded null curves immersed in C3 and SL(2,C),
    Leonor Ferrer, Francisco Martín, Masaaki Umehara and Kotaro Yamada,
    A construction of a complete bounded null curve in C3,
    preprint, math.DG/0603530 (Version 7; 02 Jan, 2013)
  • Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara and Kotaro Yamada,
    Asymptotic behavior of flat surfaces in hyperbolic 3-space,
  • Kentaro Saji, Masaaki Umehara and Kotaro Yamada,
    Ak singularities of wave fronts,
  • Kentaro Saji, Masaaki Umehara and Kotaro Yamada,
    The geometry of fronts,
  • Kentaro Saji, Masaaki Umehara and Kotaro Yamada,
    Behavior of corank one singular points on wave fronts,
  • Takeshi Sasaki, Kotaro Yamada and Masaaki Yoshida,
    Hyperbolic Schwarz map for the hypergeometric differential equation,
  • Takeshi Sasaki, Kotaro Yamada and Masaaki Yoshida,
    Derived Schwarz map of the hypergeometric differential equation and a parallel family of flat fronts,
  • Masayuki Noro, Takeshi Sasaki, Kotaro Yamada and Masaaki Yoshida,
    Confluence of swallowtail singularities of the hyperbolic Schwarz map defined by the hypergeometric differential equation,
  • Shoichi Fujimori, Kentaro Saji, Masaaki Umehara and Kotaro Yamada,
    Singularities of maximal surfaces,
  • Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara and Kotaro Yamada,
    Flat fronts in hyperbolic 3-space and their caustics,
  • Masaaki Umehara and Kotaro Yamada,
    Maximal surfaces with singularities in Minkowski space,
  • Masatoshi Kokubu, Wayne Rossman, Kentaro Saji, Masaaki Umehara and Kotaro Yamada,
    Singularities of flat fronts in hyperbolic 3-space,
  • Wayne Rossman, Masaaki Umehara and Kotaro Yamada,
    Constructing mean curvature 1 surfaces in H3 with irregular ends,
    in "Global theory of minimal surfaces", pp. 561--584, Clay Math. Proc., 2, Amer. Math. Soc., 2005.
  • Masatoshi Kokubu, Masaaki Umehara and Kotaro Yamada,
    Flat fronts in hyperbolic 3-space,
  • Wayne Rossman, Masaaki Umehara and Kotaro Yamada,
    Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature I,
  • Masatoshi Kokubu, Masaaki Umehara and Kotaro Yamada,
    An elementary proof of Small's formula for null curves in PSL(2,C) and an analogue for Legendrian curves in PSL(2,C),
  • Wayne Rossman, Masaaki Umehara and Kotaro Yamada,
    Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature II,
  • Masatoshi Kokubu, Masaaki Umehara and Kotaro Yamada,
    Minimal surfaces that attain equality in the Chern-Osserman inequality
    in "Differential Geometry and Integrable Systems", Ed. M. Guest, R. Miyaoka and Y. Ohnita, Contemporary Mathematics 308, American Mathematical Society, 2002, pp. 223-228.
  • Masatoshi Kokubu, Masaro Takahashi, Masaaki Umehara and Kotaro Yamada,
    An analogue of minimal surface theory in SL(n,C)/SU(n),
  • Masaaki Umehara and Kotaro Yamada,
    Metrics of constant curvature 1 with three conical singularities on 2-sphere,
    Illinois Journal of Mathematics, vol. 44 (2000), 72--94.
  • Shin Kato, Masaaki Umehara and Kotaro Yamada,
    General existence of minimal surfaces of genus zero with catenoidal ends and prescribed flux,
    Communications in Analysis and Geometry, vol. 8 (2000), 83--114.
  • Wayne Rossman, Masaaki Umehara and Kotaro Yamada,
    Flux for mean curvature 1 surfaces in hyperbolic 3-space, and applications,
  • Shin Kato, Masaaki Umehara and Kotaro Yamada,
    An inverse problem of the flux for minimal surfaces,
  • Wayne Rossman, Masaaki Umehara and Kotaro Yamada,
    Irreducible constant mean curvature 1 surfaces in hyperbolic space with positive genus,
    Tôhoku Mathematical Journal, vol. 49 (1997), 449--484.
  • Shin Kato, Masaaki Umehara and Kotaro Yamada,
    General existence of minimal surfaces with prescribed flux II,
    in "Topics in Complex Analysys, Differential Geometry and Mathematical Physics", (ed. S. Dimiev et. al),
    World Scientific (1997), 116--135.
  • Masaaki Umehara and Kotaro Yamada,
    A duality on CMC-1surface in the hyperbolic 3-space and a hyperbolic analogue of the Osserman Inequality,
    Tsukuba Journal of Mathematics, vol. 21 (1997), 229--237.
  • Masaaki Umehara and Kotaro Yamada,
    Another construction of a CMC-1 surface in H3,
    Kyungpook Mathematical Journal, vol. 35 (1996), 831--849.
  • Masaaki Umehara and Kotaro Yamada,
    Surfaces of constant mean curvature c in H3(-c2) with prescribed hyperbolic Gauss map,
    Mathematische Annalen, vol. 304 (1996), 203--224.
  • Masaaki Umehara and Kotaro Yamada,
    Deformation of Lie groups and their application to surface theory,
    in "Geometry and Its Applications" (ed. by T. Nagano et al.), World Scientific (1993), 241--255.
  • Masaaki Umehara and Kotaro Yamada,
    Complete surfaces of constant mean curvature-1 in the hyperbolic 3-space,
    Annals of Mathematics, vol. 137 (1993), 611--638.
  • Masaaki Umehara and Kotaro Yamada,
    A parametrization of the Weierstrass formulae and perturbation of some complete minimal surfaces of R3 into the hyperbolic 3-space,
    Journal für reine und angewandte Mathematik, vol. 432 (1992), 93--116.
  • Masaai Umehara and Kotaro Yamada,
    A deformation of tori with constant mean curvature in R3 to those in other space forms,
    Transactions of the American Mathematical Society, vol. 330 (1992), 845--857.
  • Hiroyuki Tasaki, Masaaki Umehara and Kotaro Yamada,
    Deformations of symmetric spaces of compact type to their concompact duals,
    Japanese Journal of Mathematics, vol. 17 (1991), 383--399.
  • Masaaki Umehara and Kotaro Yamada,
    Harmonic non-holomorphic maps of 2-tori into the 2-sphere,
    in "Geometry of Manifolds" (ed. by K. Shiohama), Academic Press (1989), pp. 151--160.
  • Kotaro Yamada,
    Complete space-like surfaces with constant mean curvature in the Minkowski 3-space,
    Tokyo Journal of Mathematics, vol. 11 (1988), 329--338.
  • Kotaro Yamada,
    Minimal tori in S3 whose lines of curvature lie in S2,
    Tokyo Journal of Mathematics, vol. 10 (1987), 215--226.

総論・解説

  • Wayne Rossman, Masaaki Umehara and Kotaro Yamada,
    Period problems for mean curvature one surfaces in H3 (with applications to surfaces of a low total curvature),
    Advanced Studies in Pure Mathemaatics, {\bf 51} (2008), {\sc Surveys on Gemetry and Integrable Systems}, pp. 347--399.
  • 梅原雅顕,國分雅敏,山田光太郎 (Masaaki Umehara, Masatoshi Kokubu, Kotaro Yamada)
    3次元双曲型空間における平坦な曲面
    Flat fronts in the hyperbolic 3-space (Japanese),
    「部分多様体の微分幾何学およびその周辺領域の研究」 数理解析研究所講究録 1236, 2001年11月, pp. 49--59.
    "Geometry of submanifolds and related topics" (Japanese) (Kyoto, 2001). Sūrikaisekikenkyūsho Kōkyūroku No. 1236 (2001), 49--59.
  • 山田光太郎 (Kotaro Yamada),
    双曲型空間の平均曲率 1をもつ曲面の全曲率
    Total curvature of mean curvature 1 surfaces in a hyperbolic space, (Japanese)
    「部分多様体の幾何学」 数理解析研究所講究録 1206, 2001年5月, pp. 134--143.
    "Geometry of submanifolds"(Japanese) (Kyoto, 2001), Sūrikaisekikenkyūsho Kōkyūroku No. 1206 (2001), 134--143.
  • Wayne Rossman, Masaaki Umehara and Kotaro Yamada,
    Mean curvature 1 surfaces with low total curvature in hyperbolic 3-space,
    Advanced Studies in Pure Mathematics 29, 2000, "Minimal surfaces, Geometric Analysis and Symplictic Geometry", pp. 279--297.
  • Shin Kato, Masaaki Umehara and Kotaro Yamada,
    An inverse problem of the flux formula,
    in "Proceedings of the 4th International Congress of Geometry (Thessaloniki, 1996)", 228--233,
    Giachoudis-Giapoulis, Thessaloniki, 1997.
  • 梅原雅顕・山田光太郎 (Masaaki Umehara and Kotaro Yamada),
    3次元双曲型空間の平均曲率1の曲面の幾何
    Geometry of surfaces of constant mean curvature 1 in the hyperbolic 3-space,
    数学 47 (1995), 145--157
    Sugaku Expositions, vol.10 (1997), 41--55 (translated by the authors from Japanese).
  • 梅原雅顕・山田光太郎 (Masaaki Umehara, Kotaro Yamada)
    3次元双曲型空間内の平均曲率1の曲面の双対性とその応用
    Duality of surfaces of mean curvature 1 in 3-dimensional hyperbolic spaces and its applications. (Japanese)
    「部分多様体論とその周辺」 数理解析研究所講究録 907, 1995年5月, pp. 1--11.
    "Geometry of submanifolds and related topics" (Japanese) (Kyoto, 1995). Sūrikaisekikenkyūsho Kōkyūroku No. 907 (1995), 1--11.
  • Umehara, Masaaki and Kotaro Yamada,
    Surfaces of constant mean curvature-1 in the hyperbolic 3-space,
    Geometry and global analysis (Sendai, 1993), 399--411, Tohoku Univ., Sendai, 1993.
Copyright (C) Kotaro Yamada
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