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Complex manifolds and Teichmuller spaces

Research Project

Project/Area Number 08304014
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionOsaka City University

Principal Investigator

IMAYOSHI Yoichi  Osaka City University, Faculty of Science, Professor, 理学部, 教授 (30091656)

Co-Investigator(Kenkyū-buntansha) KOMORI Yohei  Osaka City University, Faculty of Science, Assistant, 理学部, 助手 (70264794)
NISHIO Masaharu  Osaka City University, Faculty of Science, Lecturer, 理学部, 講師 (90228156)
TANIGUCHI Masahiko  Kyoto University, Garaduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50108974)
KAMIYA Sigeyasu  Okayama University of Science, Faculty of Technology, Professor, 工学部, 教授 (80122381)
NOGUCHI Junjiro  Tokyo Institute of Technology, Faculty of Science, Professor, 理学部, 教授 (20033920)
森 正気  山形大学, 理学部, 教授 (80004456)
佐官 謙一  大阪市立大学, 理学部, 助教授 (70110856)
Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1997)
Budget Amount *help
¥14,400,000 (Direct Cost: ¥14,400,000)
Fiscal Year 1997: ¥7,200,000 (Direct Cost: ¥7,200,000)
Fiscal Year 1996: ¥7,200,000 (Direct Cost: ¥7,200,000)
KeywordsTeichmuller space / complex manifold / Riemann surface / Kleinian group / quasiconformal mapping / several complex varialbles / potential theory / value distribution theory / 多変数関数論 / 値分布論 / 等解像論
Research Abstract

The head investigator has been studying geometric and analytic objects on complex manifolds, especially on Riemann surfaces and Teichmuller spaces. In particular, using complex analysis, Kleinian groups, Teichmuller spaces, he studied Douady spaces of holomorphic maps between complex manifolds, estimates of numbers of holomorphic maps, relations between harmonic maps and holomorbhic maps, and so on. Let Hol (R,S) be the set of all non-constant holomorphic maps of a closed Riemann surface R of genus g to a closed Riemann surface S of genus g' with g', (2<less than or equal>g'<less than or equal>g'). Then an estimate of the number of elements in Hol (R,S) is obtained by topological data g and g'. Its method of proof is an area estimate by using hyperbolic geometry, Kleinian groups, and complex analysis. So this method is also applicable to the case of open Riemann surfaces of hyperbolic type. Harmonic maps between Riemann surfaces and holomorphic quadratic differentials are closely relat … More ed. From this point of view, relations between harmonic maps and holomorphic maps between Riemann surfaces are considered. It is proved that harmonic maps become holomorphic or anti-holomorphic under a certai
Komori studied semialgebraic description of Teichmuller space. Okumura obtained global real analytic angle parameters for Teichmuller spaces. Sakan considered non-quasiconformal harmonic extention. Taniguchi proved that Bloch topology of the universal Teichmuller space is equivalent to the geometric convergence in the sense of Caratheodory. Kamiya studied discrete subgroups of PSU (1,2, C)with Heisenberg translations. Masaoka obtained some important results on harmonic dimension of covering surfaces. Maitani considered ploblems on optimal embedding of Riemann surfaces.
Noguchi obtained the second main theorem of Cartan-Nevalinna theorem over function fields and its application to finiteness theorem for rational points. Toda obtained the fundamental inequality for non-degenerate holomorhic curves. Mori constructed some important examples for meromorphic maps of C^n into P^n (C) in the value distribution theorem. Nishio got a mean value property for polytemperatures. Less

Report

(3 results)
  • 1997 Annual Research Report   Final Research Report Summary
  • 1996 Annual Research Report
  • Research Products

    (65 results)

All Other

All Publications (65 results)

  • [Publications] 今吉 洋一: "An eotimate of number of non-constant holomorplic mapobetween Riemann surfaces" Topology and Teichmuller Spaces. 57-78 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 今吉 洋一: "A remark on Poincore and Bergman metrics,and harmonic and holomorphic maps on a hiemann sureface" Proceedings of the 5th International Conference on Fimite or Infimite Dimosional Complex Analysis,Beijin,China,1997. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 神谷 茂保: "Discrete subgroups of P(1,2;C)with Heisenberg translations" Proceedings of the 5th International Conference on Fimite or Infimite Dimosional Complex Analysis,Beijin,China,1997. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 奥村 善英: "Global real analytic angle paremetra for Teichmiiller spaces" J.Math.Soc.Japan. 49. 213-229 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 小森 洋平: "Semialgebraic Description of Teichmiiller Space" Publication of R.I.M.S.Kyoto Univ.33(4). 527-571 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 佐官 謙一: "A note on non-quasiconformal harmonic extensions" Bull.Sox.Sci.Lettres,Sirie:Recherches surles diformations 23,Todz47. 47. 51-63 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 谷口 雅彦: "Bloch topology of the universal Teichmiiller space" Topology and Teichmiiller Spaces. 279-293 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 戸田 暢茂: "On the fundamental imequality for non-degenerate holom orphic curves" Kodai math.J. 29. 178-196 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 西尾 昌治: "A general form of a mean value property for polytemperatures on a strip domain" Proc.of the 7th International Colloquuium on Differential Equations. 269-276 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 野口 潤次郎: "Nevalima-Cartan theory over function fields and a Diophartine equation" J.reine angew,Math.487. 61-83 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 米谷 文男: "What is an optimal embedding?" Proc.of the 5th International Conference on Fimite on Infimite Dimersional Complex Anchysis,Beijin,China,1997. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 正岡 弘照: "Harmonic dimension of convering surfaces and minimal fine neighforhood" Osaka J.Math.34. 659-672 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 森 正気: "Elimination of defects of meromorphic moyysings of C^m into P^m(C)" Ann.Acad Sci.Fenn.(発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 今吉 洋一: "複素関数概説" サイエンス社, 195 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 小林 昇治: "応用数学" 近代科学社, 197 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 谷口 雅彦: "The Theory of Kleinian Groups" Oxford University Press(印刷中),

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 野口 潤次郎: "Introduction to Complex Analysis" Amer.Math.Soc., 250 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 奥村 善英: "双曲幾何学への招待" 培風館, 192 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Imayoshi, Y.: "An estimate of the number of non-constant holomorphic maps between Riemann surfaces" Topology and Teichmuller Spaces World Scientific. 57-78 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Imayoshi, Y.: "A remark on Poincare and Bergman metrics, and harmonic and holomorphic maps on a Riemann surface" Proceedings of the 5th International Conference on Finite or Infinite Dimensional Complex Analysis, Beijing, China. (to appear). (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Kamiya, S.: "Discrete subgroups of P (1,2, C) with Heisenberg translations" Proceedings of the 5th International Conference on Finite or Infinite Dimensional Complex Analysis, Beijing, China. (to appear). (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Okumura, Y.: "Global real analytic angle parameters for Teichmuller spaces" J.Math.Soc.Japan. 49. 213-229 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Komori, Y.: "Semialgebraic Description of Teichmuller space spaces" Publ.of R.I.M.S.Kyoto Univ.33. 527-571 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Sakan, K.: "A note on non-quasiconformal harmonic extensions spaces" Bull.Soc.Sci.Letters, Serie : Recherches sur les deformations. 23, Lodz 47. 51-63 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Taniguch, M.: "Bloch topology of the universal Teichmuller space" Topology and Teichmuller Spaces World Scientific. 279-293 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Toda, N.: "On the fundamental inequality for non-degenerate holomorphic curves" Kodai math.J.29. 178-196 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Nishio, M.: "A general form of a mean value property for poly-temperatures on a strip domain" Proc.of the seventh International Colloquium on Differential Equations, VSP,Utrecht. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Noguchi, J.: "Nevanlinna-Cartan theory over function fields and a Diophantine equation" J.reine angew. Math.487. 61-83 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Maitani, F.: "What is an optimal embedding?" Conference on Finite or Infinite Dimensional Complex Analysis Beijing, China. (to appear). (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Masaoka, H.: "Harmonic dimension of covering surfaces and minimal fine neighborhood" Osaka J.Math.34. 659-672 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Imayoshi, Y.: Introduction to Complex Analysis (Japanese). Science-sha, 195 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Kobayashi, S.: Applied Mathematics (Japanese). Kindaikagaku-sha, 197 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Masahiko, T.: The Theory of Kleinian Groups (to appear). Oxford Univ.Press,

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Noguchi, J.: Introduction to Complex Analysis. Amer.Math.Soc., 250 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Okumura, H.: Introduction to Hyperbolic Geometry (Japanese). Baihu-kan, 192 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 今吉洋一: "An eotimate of number of non-constant holomorphic maps between Riemann surfaces" Topology and Teichmuller Spaces. 57-78 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] 今吉洋一: "A remark on Poincome and Bergman metuca,and harmonic and helomorphic maps on a Riemann susface" Proceedings of the 5th Intirnational Conference on Finite or Infimite Dimusional Conplex,Beijin,Chima,1997. (発表予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] 神谷茂保: "Discrete snbgrops of P(1,2;C)with Heismberg translations" Proceedings of the 5th International Conference on Fimite on Infinite Dimensional Complex Analysis,Beijin,China,1997. (発表予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] 奥村善英: "Global real analytic angle paremetera for Teichmiiller spaces" J.Math.Soc.Japan. 49. 213-229 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 小森洋平: "Semialgebraic Description of Teichmiiller Space" Publication of R.I.M.S.Kyoto Univ.33(4). 527-571 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 佐官謙一: "A note on non-quasiconfermal harmonic extensions" Bull.Soc.Sci.Lettres,Sirce,Recherches sun les leformations 23,todz47. 47. 51-63 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 谷口雅彦: "Bloch topology of the universal Teichmiiller space" Topology and Teichmiiller Spaces. 279-293 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] 戸田暢茂: "On the fundamental imequality for mon-degenerate holom arphic curves" Kodai meth.J. 29. 178-196 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 西尾昌治: "A general form of a mean value property for polytemperatures on a strip8 domain" Proc.of the 7th Internatlonal Colls quuium on Differential Equations. 269-276 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 野口潤次郎: "Nevalima-Caran theory over function fields and a Diophantine equation" J.reine angew.Math.487. 61-83 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 米谷文男: "What is an optinal embedding?" Proc of the 5th International Conference on Finite on Infinite Dimevional Complex Anclysis,Beijin,china,1997. (発表予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] 正岡弘照: "Harmonic dimension of coveing surfaces and minimal fine neighborhood" Osaka J.Math.34. 659-672 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 森 正気: "Elimiration of defects of meronaplic moppings of G^m into P^m(G)" Amm.Acad Sci.Fenn.(発表予定).

    • Related Report
      1997 Annual Research Report
  • [Publications] 今吉洋一: "複素関数概説" サイエンス社, 195 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 小林昇治: "応用数学" 近代科学社, 197 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] 谷口雅彦: "The Theory of Kleinian Groups" Oxford University Press(印刷中),

    • Related Report
      1997 Annual Research Report
  • [Publications] 野口潤次郎: "Introduction to Complex.Analysis" Amer.Math.Soc., 250 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 奥村善英: "双曲幾何学への招待" 培風館, 192 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] Y. Imayoshi: "An estimate of the number of non-constant holomorphic maps between Riemann surfaces" Topology and Teichmiiller Spaces, World Scientific. 57-78 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] J. Noguchi: "A construction of hyperbolic hyper surfaces of P^n (C)" Math. Ann. 304. 339-362 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] N. Toda: "On the order of holomorphic curves with mascimal deficiency sum" Kodai Math. J.18-3. 451-474 (1995)

    • Related Report
      1996 Annual Research Report
  • [Publications] F. Maitani: "Rectilimean slit conformal mappings" J. Math. Kyoto Univ.(to appear).

    • Related Report
      1996 Annual Research Report
  • [Publications] M. Taniguchi: "Bloch topology of the universal Teichmiiller space" Topology and Teichmiiller Spaces, World Scientific. 279-293 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y. Komori: "On the monotonicity of topological entropy for bimodal read cubic maps" 数理解析研究所講究録. 938. 26-33 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] K. Sakan: "Harmonic and quaoicrenformal mappings which agree on the boundary" Ann. Univ. Marie Curie-Sklodowska. 49. 159-171 (1995)

    • Related Report
      1996 Annual Research Report
  • [Publications] S. Kamiya: "Parabolic elements of U (1, n ; C)" Revue Roumaine de Mathmatiques Pures et Appliques. 40-1. 55-64 (1995)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y. Okumura: "Global real analytic length parameters for Teichmiiller spaces" Hiroshima Math. J.26. 165-179 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] M. Nishio: "A mean value property of poly-temperatures on a strip domain" J. London Math. Soc.(to appear).

    • Related Report
      1996 Annual Research Report
  • [Publications] H. Masaoka: "Criterion of Wiener type for minimal thinneso on covering surfaces" Proc. Japan Acad. 72. 154-156 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 谷口雅彦: "双曲幾何への招待" 培風館, 185 (1996)

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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