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1998 Fiscal Year Final Research Report Summary

Geometry related to harmonic maps

Research Project

Project/Area Number 09640092
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionTOKYO INSTITUTE OF TECHNOLOGY

Principal Investigator

MIYOOKA Reiko  Guraduate School of Science and Engineering TOKYO INSTITUTE OF TECHNOLOGY,Assistant Professor, 大学院・理工学研究科, 助教授 (70108182)

Co-Investigator(Kenkyū-buntansha) TSUJI Hajime  Graduate School of Science and Engineering TOKYO INSTITUTE OF TECHNOLOGY,Assista, 大学院・理工学研究科, 助教授 (30172000)
KOTANI Motoko  Toho University, Faculty of Science, Assistant Professor, 理学部, 助教授 (50230024)
OHNITA Yoshihiro  Tokyo Metropolitan University, Faculty of Science, Professor, 理学部, 教授 (90183764)
ITO Hidekazu  Graduate School of Science and Engineering (TOKYO INSTITUTE OF TECHNOLOGY) ; Ass, 大学院・理工学研究科, 助教授 (90159905)
FUTAKI Akito  Guraduate School of Science and Engineering TOKYO INSTITUTE OF TECHNOLOGY,Profes, 大学院・理工学研究科, 教授 (90143247)
Project Period (FY) 1997 – 1998
Keywordsharmonic maps / comstant mean curvature surfaces / minimal surfaces / isparametric hypersurfaces / Integrable systems / Value distributions / Gauge theory / Seiberg-witten equation
Research Abstract

Main results in the surface theory (Miyaoka, Koiso, Sato, Masuda, Cheng), the theory of hypersurfaces (Miyaoka), the theory of integrable systems (Miyaoka, Ito, Ohnita, Udagawa), the theory of harmonic maps on lattices and graphs (Kotani), the theory of Gauge theoretic harmonic maps (Ohnita, Hashiguchi), the theory of Lie group and symmetric spaces (Hattori, Tanaka), stochastic value distribution theory (Atsuji), Differential topological invariant via Seiberg-Witten equation (Futaki), application of multiplier ideal sheaves (Tsuji), are as follows :
Miyaoka characterized non-conformal harmonic maps as components of minimal surfaces, constructed examples of global deformations of non-conformal harmonic maps from compact Riemann surfaces into 5-dimensional sphere, giving a lower estimate of the nullity, and gave a global correspondence between constant mean curvature surfaces in 3-dimensional sphere and a pair of non-conformal harmonic maps into 2-spheres. She showed the homogeneity of is … More oparametric hypersurfaces with six principal curvatures, applying the isospectral principle and Singer's theorem, introduced Ferapontov's results on the relation with the integrability theory of Hamiltonia system of hydrodynamic type, and Terng-Uhlenbecks' explanation of scattering method, hierarchy, and Backlund transformation via the Poisson actions.
Futaki investigated the obstructions to the existence of Kahler-Einstein metrics or positive scalar curvature metrics, by using Seiberg-Witten equation.
Ito extended Liouvill-Arnolds' theorem into sustems such as reversible system which has singularities.
Ohnita investigated the moduli space of the solution of Gauge-theoretic equation of harmonic maps, and constructed a family of complex Lagrangean submanifolds of the hyper-Khler moduli of the solution of Hitchin's self-dual equations.
Kotani investigated the behavior of harmonic maps on crystal lattices, of the asymptotic expansion of heat kernels at infinite time, and discussed with the relation to Albanese maps.
Atusji applied value distribution of holomorphic and harmonic maps in stochastic calculus, and generalized Casorati-Weierstrass type theorem, lemma on logarithmic differential for Nevanlinna meromorphic function, etc. Less

  • Research Products

    (70 results)

All Other

All Publications (70 results)

  • [Publications] Reiko Miyaoka: "The splitting and deformation of the generalized Gauss map of compact CMC surfaces" Tohoku Math.J.51. 35-53 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 宮岡 礼子: "ポアッソン群作用と可積分系の散乱理論" 甲府報告集 : Harmonic maps, Spectral curves and Soliton Equations. 1-82 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Reiko Miyaoka: "Construction of CMC surfaces in S^3 from a pair of non-conformal harmonic maps into S^2" Proceedings of PGA98. to appear. (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Reiko Miyaoka: "Recent topics on harmonic map theory and related parts" Proceedings of the Third International Workshop on Differential Geometry. (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Reiko Miyaoka: "On the theory of integrable systems and its applications" Proceedings of the Third International Workshop on Differential Geometry. (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Atsushi Atsuji: "A remark on a limiting behavior of the occupation times on unbounded domains of Blownian motion" Jour.Math.Sci.Univ.Tokyo. to appear.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Atsushi Atsuji: "A Casorati-Weirstrass theorem for holomorphic maps and invariant σ-fields of rolomorphir diffusion" Bull.Sci.Math.to appear. (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hidekazu Ito: "Integrability of symplectic mappings and their Birkhoff normal forms" Tohoku Math.J.49. 73-114 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 伊藤秀一: "ハミルトン力学系の最近の発展について" 物性研究. 70(4). (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Seiichi Udagawa: "An exposition of Mclntosh's work by showing many examples" 日本大学医学部一般教育研究紀要. 26. 13-35 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Martin Guest & Yoshihiro Ohnita: "Actions of loop groups, deformations of harmonic maps, and their applications, to appear in Sugaku Expositions" English translation In “Selected Papers on Harmonic Analysis, Groups and Invariants", Amer.Math.Soc.Translations Ser.2. 183. 33-50 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Miyuki Koiso: "Applications of the maximum principle to surfaces with constant mean curvature" 京都大学数理解析研究所講究録. 995. 1-6 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Miyuki Koiso: "The stability and the vision number of surfaces with constant mean curvature" Bulletin of Kyoto University of Education. B92. 1-11 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Miyuki Koiso: "The uniqueness for stable surfaces of constant mean curvature with free boundary" Bulletin of Kyoto University of Education. B94. 1-7 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Motoko Kotani: "Harmonic 2-spheres with γ pairs of extra eigenfunctions" Proc.Amer.Math.Soc.125. 2083-2092 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Motoko Kotani: "Asymptotic behavior of the transition probability of a randon walk on an infinite graph with T.Shirai and T.Sunada." J.Funct.Anal.159. 664-689 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Motoko Kotani: "Jacobian tori associated with afinite graph and its abelian covering graphs, with T.sunada" to appear, Adv.in Apply.Math.(1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Wayne Rossman and Katsunori Sato: "Constant Mean Curvature Surfaces with Two Ends in Hyperbolic Space" Experimental Mathematics. 7, No.2. (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Qing-Ming Cheng and Katsuhiro Shiohama: "Non-existence of stable currents II." Kyushu J.Math.51. 149-164 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Qing-Ming-Cheng and Susumu Ishikawa: "Spacelike hypersurfaces with constant scalar curvature" Monu Scripta Math.95. 499-505 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hongcang Yang and Qing-Ming Cheng: "Chern's conjecture on minimal hypersurfaces" Math.Z. 227. 377-390 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Qing-Ming Cheng, Yoshiroh Machiga-Shira and Yoshihiro Sugioka: "The relation between degree and dilatation of continuous maps" Japanese J.Math.24. 183-190 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Qing-Ming Cheng and Susumu Ishikawa: "A characterization of the Clifford torus" Proc.Amer.Math.Soc.127. 819-828 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Qing-Ming Cheng: "Complete maximal spacelike surfaces in an anti-de Sitter space H^4_2(C)" to appear in Glasgow Math.J.(2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Qing-ming Cheng, Susumu Ishikawa and Katsuhiro Shiohama: "Conformally flat 3-manifolds with constant scalar curvature" J.Math.Soc.Japan. 51. 209-226 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hajme Tsuji: "Existence and applications of analytic Zariski decomposition" to appear, Prc.of 40-th Taniguchi Conference.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Junjiro Noguchi: "Nevalinna-Cartan theory over function fields and a Diophatine equation" J.reine angew.Math.487. 61-83 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Junjiro Noguchi: "On holomorphic curves in sem-Abelian varieties" Math.Z.228. 713-721 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hideko Hashiguchi: "The uniton numbers of the harmonic 2-spheres in Gr_2(C^7)" J.Math.Soc.Japan. 49-1. 81-105 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tadashi Nagano, Makiko Tanaka: "The involutions of compact Symmetric Spaces, IV." to appear, Tokyo J.Math.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 伊藤秀一: "常微分方程式と解析力学" 共立出版, (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 二木昭人: "サイバーグ・ウィッテン不変量とトポロジー" 培風館, (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Junjiro Noguchi: "Amer.Math.Soc.Rhode Island" Introduction to Complex Analysis, MMONO 168, (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 二木昭人: "培風館" 基礎講義線形代数学, (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Reiko Miyaoka: "The splitting and deformations of the generalized Gauss map of compact CMC surfaces" Tohoku Math.J.51. 35-53 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Reiko Miyaoka: "Poisson actions and scattering theory of integrable systems" Proceedings of Kofu meeting : Harmonic maps, Spectral curves and Soliton Equations. 1-82 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Reiko Miyaoka: "The splitting and deformations of the Gauss map of compact CMC surfaces, to appear" Proceedings of Brest Workshop 1997 : Harmonic Morphism, Harmonic Maps and Related Topics. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Reiko Miyaoka: "Construction of CMC surfaces in S^3 from a pair of nonconformal harmonic maps into S^2" Proceedings of DGA98(1998), Brno, Czecho. (to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Reiko Miyaoka: "Recent topics on harmonic map theory and related parts, to appear" Proceedings of The Third International Workshop on Differential Geometry1998, Kyungpook Univ., Korea. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Reiko Miyaoka: "On the theory of integrable systems and its applications, to appear" Proceedings of The Third International Workshop on Differential Geometry(1998), Kyungpook Univ., Korea. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Atsushi Atsuji: "A remark on a limiting behavior of the occupation times on unbounded domains of Brownian motion" Jour.Math.Sci.Univ, Tokyo. (to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Atsushi Atsuji: "A Casorati-Weierstrass theorem for holomorphic maps and invariant sigma-fields of holomorphic diffusions" Bull.Sci.Math.(to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hidekazu Ito: "Integrability of symplectic mappings and their Birkhoff normal forms normal forms" Tohoku Math.J.49. 73-114 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hidekazu Ito: "Recent development of Hamiltonian dynamics" Bussei-kenkyu. 70(4). (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Seiichi Udagawa: "An exposition of McIctosh's work by showing many examples" Reseach Report of Nichidai-Igakubu. 26. 13-35 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Martin Guest and Yoshihiro Ohnita: "Actions of loop groups, deformations of harmonic maps, and their applications, to appear in Sugaku Expositions, (English translation)" "Selected Papers on Harmonic Analysis, Groups and Invariants", Amer.Math.Soc.Translations Ser.2. 183. 33-50 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Miyuki Koiso: "Applications of the maximum principle to surfaces with constant mean curvatute" Proceedings of RIMS. 995. 1-6 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Miyuki Koiso: "The stability and the vision number of surfaces with constant mean curvature" Bulletin of Kyoto University of Education. B92. 1-11 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Miyuki Koiso: "The uniqueness for stablesurfaces of constant mean curvature with free boundary" Bulletin of Kyoto University of Education. B94. 1-7 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Motoko Kotani: "Harmonic 2-spheres with gamma pairs of extra eigenfunctions" Proc.Amer.Math.Soc.125. 2083-2092 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Motoko Kotani: "Asymptotic behavior of the transition probability of a random walk on an infite graph, with T.Shirai and T.Sunada" J.Funct.Anal.159. 664-689 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Motoko Kotani: "Jacobian tori associated with a finite graph and its abelian covering graphs, with T.Sunada" Adv.in Apply.Math. (to appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Wayne Rossman and Katsunori Sato: "Constant Mean Curvature Surfaces with Two Ends in Hyperbolic Space" Experimental Mathematics. 7, No.2. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Qing-Ming Cheng and Katsuhiro Shiohama: "Non-existence of stable currents II" Kyushu J.Math. 51. 149-164 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Qing-Ming Cheng and Susumu Ishikawa: "Complete maximal spacelike submanifolds" Kodai Math.J.20. 208-217 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Qing-Ming Cheng and Susumu Ishikawa: "Spacelike hypersurfaces with constant scalar curvature" Manuscripta Math.95. 499-505 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hongcang Yang and Qing-Ming Cheng: "Chern's conjecture on minimal hypre-surfaces" Math.Z.227. 377-390 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Qing-Ming Cheng, Yoshiroh Machigashira and Yoshihiro Sugioka: "The relation between degree and dilatation of continuous maps" Japanese J.Math.24. 183-190 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Qing-Ming Cheng and Susumu Ishikawa: "A Characterization of the Clifford torus" Proc.Amer.Math.Soc.127. 819-828 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Qing-Ming Cheng, Susumu Ishikawa and Katsuhiro Shiohama: "Conformally flat 3-manifolds with constant scalar curvature" J.Math.Soc.Japan. 51. 209-226 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Qing-Ming Cheng: "Complete maximal spacelike surfaces in an anti-de Sitter apace H^4_(c)" Glasgow Math.J.(to appear). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hajime Tsuji: "Existence and applications of analytic Zariski decomposition" Proc.of 40-th Taniguchi Conference.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Junjiro Noguchi: "Nevalinna-Cartan theory over function fields and a Diophatine equation" J.reine angew.Math.487. 61-83 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Junjiro Noguchi: "On holomorphic curves in semi-Abelian varieties" Math.Z.228. 713-721 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hideko Hashiguchi: "The uniton numbers of the harmonic 2-spheres in Gr_2(C^4)" J.Math.Soc.Japan. 49-1. 81-105 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tadashi Nagano and Makiko Tanaka: "The involutions of compact symmetric spaces, IV" Tokyo J.Math.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Junjiro Noguchi: Introduction to Complex Analysis. MMONO 168, Amer.Math.Soc.Rhode Island, (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hidekazu Ito: Ordinary differential equations and analytic dynamics. Kyoritsu-publ., (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Akito Futaki: Seiberg-Witten invariants and topology, (trans). Basifu-kan, (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Akito Futaki: Lecture on linear algebra. Baifu-kan, (1998)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1999-12-08  

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