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Teichmuller Spaces and Mapping Class Groups

Research Project

Project/Area Number 10440059
Research Category

Grant-in-Aid for Scientific Research (B).

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
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) SAKAN Ken-ichi  Osaka City University, Faculty of Science, Associate Professor, 理学部, 助教授 (70110856)
KAWAUCHI Akio  Osaka City University, Faculty of Science, Professor, 理学部, 教授 (00112524)
KASUE Atsushi  Osaka City University, Faculty of Science, Professor, 理学部, 教授 (40152657)
NOGUCHI Junjiro  University of Tokyo, Graduate School of Math. Science, Professor, 大学院・数理科学研究科, 教授 (20033920)
KOMORI Yohei  Osaka City University, Faculty of Science, Lecturer, 理学部, 講師 (70264794)
谷口 雅彦  京都大学, 大学院・理学研究科, 助教授 (50108974)
金信 泰造  大阪市立大学, 理学部, 助教授 (00152819)
Project Period (FY) 1998 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 2000: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1999: ¥2,000,000 (Direct Cost: ¥2,000,000)
KeywordsTeichmuller space / Riemann sueface / Kleinian group / quasi-conformal mapping / mapping class group / Teichmuller modular group / holomorphic mapping / harmonic mapping / 正則族 / モデュライ空間 / 複素多様体 / 正則2次微分
Research Abstract

Mainly we studied the following three themes :
1. By using Bers-Thurston classification of elements of mapping class groups, we determined types of elements of monodormy groups of holomorphic families of Riemann surfaces, especially induced by Kodaira surfaces.
2. We gived a condition for harmonic maps between compact hyperbolic Riemann surfaces so that they are holomorphi or anti-holomorphic.
3. We gave an estimate of the number of non-constant holomorphic maps between compact hyperbolic Riemann surfaces by topological data.

Report

(4 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • Research Products

    (83 results)

All Other

All Publications (83 results)

  • [Publications] Yoichi Imayoshi: "The Nielsen-Thurston-Sers type of elementy of the monodromy group of a holomorphic family of Riemann surfaces induced by a kodainn"Lecture Notes in Pure and Applied Mathematics, Marcel Dekker. 214. 169-177 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yoichi Imayoshi: "A remank on the Bess type of some self-maps of Riemann surfaces with two specified plonts"International Society for Analysis, Applications and Computation, Kluwer. 8. 871-875 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yoichi Imayoshi: "A remark on Ionicare and Bergman metrics, and hamonic and holom siphic maps on a Riemann surface"Proc.of the 5th.International Conference on finite and Infinite dimensional complex analysis. 117-122 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Atsushi Kasue: "Convergence of Riemannian manifolds, Laplace operators and energy forms"proc. of 5th.Pacific Rim Geometric Conference. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Atsushi Kasue: "Convergence of Riemannian manifolds and Laplace operators; I"Ann.Institut Fourier. (発表予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Shim Kato: "Genetic syistence of minimal surfaces of genus gene with catonoidal endo and prescribed flux"Comm.Anal.Geom.. 8. 83-114 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Taizo Kanenobu: "An unknatting operation on siffon 2-knots"J.Knat Theory Ramification. 9. 1101-1028 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Akio Kawauchi: "Floer homology of topological imitations of homology 3-spheres"J.Knot Theory Ramifications. 7. 41-60 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Akio Kawauchi: "The quadratic form of link"Contemp.Math.. 233. 97-116 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Ken-Ichi Sakan: "A conformal invariant dilation of quaoisymmetry"Ann.Univ.Masiae Curie-Sklodowska Sect.A. 53. 167-181 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yohei Komori: "The Riley slice revisited"Geometry and Topology Monography. 1. 303-316 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Masahiko Taniguchi: "A condition of quasi conformal extendofility"Proc.Japan Acad.Ser A.Math.Sci.. 75. 58-60 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Masaharu Niohio: "A mean value property of poly-temperatures on a strip domain"J.London Math.Soc(2). 58. 381-393 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Masaharn Nishio: "Note on poly-supertemperatures on a strip domain"Osaka J.Math.. 36. 539-556 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Junjiro Noguchi: "The value distribution of holomorphic curver into semi-Abelian varieties"C.R.Acad.Sci.Pari,Seri I. 331. 235-240 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [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(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Fumio Maitani: "Conformal welding of annuli"Osaka J.Math.. 35. 579-591 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Fumio Maitani: "Behavior of Bergman metric under quasi conformal mappings"Proc.of the 6th.International Conference on finite and Infinite dimensional complex analysis. 169-175 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Masahiko Taniguchi: "Holomorphic Dynamics"Cambridge Univ.Press. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Masahiko Taniguchi: "Hyperfrolic manifolds and Kleinian Groups"Oxford Univ.Press. (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Junichino Noguchi: "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
      2000 Final Research Report Summary
  • [Publications] Y.Imayoshi: "The Nielsen-Thurston-Bers type of elements of the monodromy group of a holomorphic family of Riemann surfaces induced by a Kodaira surface I"Lecture Notes in Pure and Applied Mathematics, Marcel Dekker. Vol.214. 169-177 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Imayoshi: "A remark on the Bers type of some self-maps of Riemann surfaces with two specified points"Proc. of the Second ISSAC Congress, International Society for Analysis, Applications and Computation, Kluwe. Vol.8. 871-875 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] "A remark on Poincare and Bergman metrics, and harmonic and holomorphic maps on a Riemann surface"Proc. of the 5th International Conference on Finite or Infinite Dimensional Complex Analysis. 117-122 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] A.Kasue: "Convergence of Riemannian manifolds, Laplace operators and energy forms"Proc. of the fifth Pacific Rim Gemetric Conference, Tohoku Mathematical Publications. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] A.Kasue: "Convergence of Riemannian manifolds and Laplace operators ; I"Ann.Institut Fourier. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] "General existence of minimal surfaces of genus zero with catenoidal ends and prescribed flux"Comm.Anal.Geom.. 8. 83-114 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] "An unknotting operation on ribbon 2-knots"J.Knot Theory Ramifications. 9. 1011-1028 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] A.Kawauchi: "Floer homology of topological imitations of homology 3-sphere"J.Knot Theory Ramifications. 7. 41-60 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] A.Kawauchi: "The quadratic form of a link"Contemp.Math.. 233. 97-116 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Sakan: "A conformally invariant dilatation of quasisymmetry"Ann.Univ.Mariae Curie-Sklodowska Sect.. A 53 1999. 167-181 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Komori: "The Riley slice revisited"Geometry and Topology Monographs. Vol.1. 303-316 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Taniguchi: "A condition of quasiconformal extendability"Proc.Japan Acad.Ser.A Math.Sci.. 75. 58-60 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Nishio: "A mean value property of poly-temperatures on a strip domain"J.London Math.Soc. (2). 58. 381-393 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Nishio: "Note on Poly-supertemperatures on a strip domain"Osaka J.Math.. 36. 539-556 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] J.Noguchi: "The value distribution of holomorphic curves into semi-Abelian varieties"C.R.Acad.Sci., Serie I. 331. 235-240 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] J.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
    • Related Report
      2000 Final Research Report Summary
  • [Publications] F.Maitani: "Conformal welding of annuli"Osaka J.Math.. 35. 579-591 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] F.Maitan: "Behavior of Bergman metric under quasiconformal mappings"Proc.of the 6th International Colloquiumon Finite or Infinite Dimensional Complex Analysis. 169-175 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yoichi Imayoshi: "The Nielsen-Thurston-Bers type elemanty of the monodromy group of a holomorphic family of Riemann surfacers induced by a Kodain surface I."Lecture Notes in Pure and Applied Mathematics, Marcal Dekker. 214. 169-177 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Yoichi Imayoshi: "A remark on the Bers type of some self-maps of Riemann surfaces with two specified points"International Society for Analysis, Applications and Computation, Kluwer. 8. 871-875 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Yoichi Imayoshi: "A remark on foincare and Bergman metrics, and harmonic and holomorphic maps on a Riemann surface"Proc.of the 5th.International Conference on finite and Infinite dimensional complet analysis. 117-122 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] Atsushi Kasue: "Convergence of Riemannian manifolds, Laplace operators and energy forms"Proc.of 5th. Pacific Rim Geometric Conference. (発表予定).

    • Related Report
      2000 Annual Research Report
  • [Publications] Atsushi Kasue: "Convergence of Riemannian manifolds and Laplace operators ; I"Ann.Institut Fourier. (発表予定).

    • Related Report
      2000 Annual Research Report
  • [Publications] Shin Kato: "Generic existence of minimal surfaces of genus gene with catenoidal ends and prescribed flux"Comm.Anal.Geom.. 8. 83-114 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Taizo Kanenobu: "An unknotting operation on riffon 2-knots"J.Knot Theory Ramifications. 9. 1101-1028 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Akio Kawauchi: "Floer homology of topological imitations of homology 3-spheres"J.Knot Theory Ramifications. 7. 41-60 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] Akio Kawauchi: "The quadratic form of link"Contemp.Math.. 233. 97-116 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] Ken-Ichi Sakan: "A conformal invariant dilation of quasisymmetry"Ann.Univ.Mariae Cuire-Sklodowska Sect.A. 53. 167-181 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] Yohei Komori: "The Riley slice revisited"Geometry and Topology Monographs. 1. 303-316 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] Masahiko Taniguchi: "A condition of quasi conformal extendability"Proc.Japan Acad.Ser.A.Math.Sci.. 75. 58-60 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] Masaharu Nishio: "A mean value property of poly-temperatures on a strip domain"J.Lodon Math.Soc (2). 58. 381-393 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] Masaharu Nishio: "Note on poly-supertemperatures and strip domain"Osaka J.Math.. 36. 539-556 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] Junjiro Noguchi: "The value distribution of holomorphic curves into semi-Abelian varieties"C.R.Acad.Sci.Pari,Seri I. 331. 235-240 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Junjiro Noguchi: "On holomorphic curves in semi-Abelian varieties"Math.Z.. 228. 713-721 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] Fumio Maitani: "Conformal welding of annuli"Osaka J.Math.. 35. 579-591 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] Fumio Maitani: "Behavior of Bergman metric under quasiconformal mappings"Proc.of the 6th.International conference on finite and Infinite dimensional complex analysis. 169-175 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] Masahiko Taniguchi: "Holomorphic Dynamics"Cambridge Univ.Press. (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] Masahiko Taniguchi: "Hyperbolic manifolds and Kleinian Groups"Oxford Univ.Press. (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] Junichiro Noguchi: "Introduction to Complex Analysis"Amer.Math.Soc.. 250 (1997)

    • Related Report
      2000 Annual Research Report
  • [Publications] Y. Imayoshi: "A remark on monodromy of a holomosphic family of Riemann surface incluced by a Kodaira surface and the Nielsen-Thurston* Bers cla*ification"The Proceedings of the 7th International Colloquium on Finite and Infinite Dimensional Complex Analysis. 単項本(近刊).

    • Related Report
      1999 Annual Research Report
  • [Publications] Y. Imayoshi: "A remark an the Bers type of some self-maps of Riemann surfaces with two specifted pochts"The Proceedings of the Second Congress ISSAC 1999. 単項本(近刊).

    • Related Report
      1999 Annual Research Report
  • [Publications] J. Noguchi: "On holomorphic curves in semi-Abelian varieties"Math. Z. 228. 713-721 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] A. Kasue: "Riemannian submersion* and isoperimetric-in equalities"Geometriae Dedicata. 70. 24-47 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] M. Nishio: "A mean value property of poly-temperatures on a strip doma"J. London Math. Soc.. (近刊).

    • Related Report
      1999 Annual Research Report
  • [Publications] M. Nishio: "Note on poly-supertemperatures on a strip domain"Osaka J. Math.. (近刊).

    • Related Report
      1999 Annual Research Report
  • [Publications] T. Kanenobu: "Va*iliev link invariants of order three"J. Knot Theory Ramifications. 7. 433-462 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] T. Kanenobu: "Recuroive calculation for an invariant of a ribon knot"J. Knot Theory Ramifications. (近刊).

    • Related Report
      1999 Annual Research Report
  • [Publications] S. Kato: "Uniquenes of solutions of an elliptic singular boundory value problem"Osaka J. Math.. 35. 279-302 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Mi Taniguchi: "On topological completeness of decoiated exponential families"Sci. Bull. of Josai Univ. 4. 1-10 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] K. Matsugaki: "Hyperbolic manifolds and Kleinian groups"Oxford University Press. 253 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Yoichi Imayoshi: "A remark on Poincare and Bergman metrics,and harmonic and holomorphic maps an a Riemann surface" The Proceedings of the 5th International conference on Finits or Infinite Dimensional Complex Analysis. 117-122 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Yohei Komori: "The Riley slice revised" Geometry & Topology Monograph. 1. 303-316 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Ken-ichi Sakan: "The harmonic and quasi conformal extension operators" Banach Center Publications. (出版予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] Masaharu Nishio: "A mean value property of poly-temperatures on a strip domain" J.London Math.Soc.(出版予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] Atsushi Kasue: "Riemannian submersians and isoperimetric in equalities" Geometriae Dedicata. 70. 27-47 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Shin Kato: "Uniqueness of solutions of an elliptic singular boindary value problem" Osaka Math.J. 35. 279-302 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Akio Kawauchi: "Floer homology of topological imitations of homology 3-spheres" J.Knot Theory Ramifications. 7. 41-60 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Taizo Konenobu: "Vasiliev invariants of order three" J.Knot Theory Ramifications. 7. 433-462 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Junjiro Noguchi: "On holomophic curves in semi-Afelian varieties" Math.Z.228. 713-721 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Junjiro Noguchi: "Nevalinna-Cartan theory over function field and Diophantine equetian" J.reine angew.Math.487. 61-83 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] 今吉洋一: "複素関数概説" サイエンス社, 195 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Junjiro Noguchi: "Introduction to Complex Analy" American Mathematical Society, 250 (1998)

    • Related Report
      1998 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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