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Analysis of structures of infinite dimensional Teichmuller spaces and complex analytic moduli spaces

Research Project

Project/Area Number 20740072
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionChiba University

Principal Investigator

FUJIKAWA Ege  Chiba University, 大学院・理学研究科, 准教授 (80433788)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsリーマン面 / タイヒミュラー空間 / モジュライ空間 / 複素解析学 / タイヒミュラー空間論 / 擬等角写像 / 写像類群
Research Abstract

For research of the infinite dimensional Teichmuller space of an analytically infinite Riemann surface, we consider the asymptotic Teichmuller space which is a quotient space of the Teichmuller space. A quasiconformal mapping class of a Riemann surface acts on the asymptotic Teichmuller space biholomorphically as an asymptotic Teichmuller modular transformation, but it can act trivially, which is different from the case of the Teichmuller space. In this research, we gave a characterization of the asymptotically trivial mapping class group. Furthermore, we proved the fixed point theorem for the asymptotic Teichmuller modular group and gave an answer to the asymptotic version of the Nielsen realization problem.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (37 results)

All 2011 2010 2009 2008 Other

All Journal Article (15 results) (of which Peer Reviewed: 15 results) Presentation (19 results) Book (2 results) Remarks (1 results)

  • [Journal Article] Stable quasiconformal mapping class groups and asymptotic Teichmuller spaces2011

    • Author(s)
      Ege Fujikawa, Katsuhiko Matsuzaki
    • Journal Title

      American Journal of Mathematics 133

      Pages: 637-675

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Structure theorem for holomorphic self-covers and its applications, Infinite dimensional Teichmuller space and moduli space2010

    • Author(s)
      Ege Fujikawa, Katsuhiko Matsuzaki, Masahiko Taniguchi
    • Journal Title

      RIMS Kokyuroku Bessatsu B 17

      Pages: 21-36

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Elliptic modular transformations on Teichmuller and asymptotic Teichmuller spaces, Infinite dimensional Teichmuller space and moduli space2010

    • Author(s)
      Ege Fujikawa
    • Journal Title

      RIMS Kokyuroku Bessatsu B 17

      Pages: 1-20

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Limit set of quasiconformal mapping class group on asymptotic Teichmuller space2010

    • Author(s)
      Ege Fujikawa
    • Journal Title

      Teichmuller theory and moduli problem, Lecture note series in the Ramanujan Mathematical Society No.10

      Pages: 167-178

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Elliptic modular transformations on Teichmuller and asymptotic Teichmuller spaces2010

    • Author(s)
      Ege Fujikawa
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B17 Pages: 1-20

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Structure theorem for holomorphic self-covers and its applications2010

    • Author(s)
      Ege Fujikawa, Katsuhiko Matsuzaki, Masahiko Taniguchi
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B17 Pages: 21-36

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The projection of limit sets of modular groups on asymptotic Teichmuller spaces2009

    • Author(s)
      Ege Fujikawa, Katsuhiko Matsuzaki
    • Journal Title

      Proceedings of the 16th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, Dongguk University, Daeyang Printing

      Pages: 86-92

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The projection of limit sets of modular groups on asymptotic Teichmuller spaces2009

    • Author(s)
      Ege Fujikawa, Katsuhiko Matsuzaki
    • Journal Title

      Proceedings of the 16th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications

      Pages: 86-92

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Structure theorem for holomorphic self-covers and its applications2009

    • Author(s)
      Ege Fujikawa,Katsuhiko Matsuzaki and Masahiko Taniguchi
    • Journal Title

      RIMS Kokyuroku Bessatsu (to appear)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pure mapping class group acting on Teichmuller space2008

    • Author(s)
      Ege Fujikawa
    • Journal Title

      Conformal Geometry and Dynamics 12

      Pages: 227-239

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dynamics on Teichmuller spaces and self-covering of Riemann surfaces2008

    • Author(s)
      Ege Fujikawa, Katsuhiko Matsuzaki, Masahiko Taniguchi
    • Journal Title

      Mathematische Zeitschrift 260

      Pages: 865-888

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Elliptic quasiconformal mapping classes acting on asymptotic Teichmuller spaces2008

    • Author(s)
      Ege Fujikawa, Katsuhiko Matsuzaki
    • Journal Title

      Proceedings of the 15th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, Osaka Municipal Universities Press

      Pages: 169-173

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Pure mapping class groups acting on Teichmuller spaces2008

    • Author(s)
      Ege Fujikawa
    • Journal Title

      Conformal Geometry and Dynamics 12

      Pages: 227-239

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stable quasiconformal mapping class groups and asymptotic Teichmuller spaces

    • Author(s)
      Ege Fujikawa, Katsuhiko Matsuzaki
    • Journal Title

      American Journal of Mathematics (to appear)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Limit set of quasiconformal mapping class group on asymptotic Teichmuller space

    • Author(s)
      Ege Fujikawa
    • Journal Title

      Lecture note series in the Ramanujan Mathematical Society (to appear)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Asymptotic Nielsen realization problem and stable quasiconformal mapping class group2010

    • Author(s)
      Ege Fujikawa
    • Organizer
      Teichmuller theory
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach
    • Year and Date
      2010-12-01
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] The fixed point theorem and the Nielsen realization problem for asymptotic Teichmuller modular groups2010

    • Author(s)
      Ege Fujikawa
    • Organizer
      Complex Analysis and Dynamics Seminar
    • Place of Presentation
      City University of New York
    • Year and Date
      2010-10-29
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] The fixed point theorem for asymptotic Teichmuller modular groups2010

    • Author(s)
      Ege Fujikawa
    • Organizer
      The 18th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Place of Presentation
      University of Macau
    • Year and Date
      2010-08-14
    • Related Report
      2010 Annual Research Report
  • [Presentation] 漸近的タイヒミュラーモジュラー群に対するニールセン実現問題2010

    • Author(s)
      藤川英華
    • Organizer
      リーマン面・不連続群論研究集会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-01-11
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] The fixed point theorem for asymptotic Teichmuller modular groups2010

    • Author(s)
      Ege Fujikawa
    • Organizer
      the 18th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Place of Presentation
      University of Macau
    • Related Report
      2010 Final Research Report
  • [Presentation] Nielsen realization problem for asymptotic Teichmuller modular groups2010

    • Author(s)
      Ege Fujikawa
    • Organizer
      Workshop on Geometry, Topology and Dynamics of Character Varieties
    • Place of Presentation
      National University of Singapore
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] The Nielsen realization problem for asymptotic Teichmuller modular groups2010

    • Author(s)
      藤川英華, 松崎克彦
    • Organizer
      日本数学会2010年年会函数論分科会
    • Place of Presentation
      慶応義塾大学
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] infinite dimensional Teichmuller space and moduli space, RIMS Kokyuroku Bessatsu B172010

    • Author(s)
      藤川英華 editor
    • Organizer
      Research Institute for Mathematical Sciences
    • Place of Presentation
      Kyoto University
    • Related Report
      2010 Final Research Report
  • [Presentation] リーマン面の正則被覆とタイヒミュラー空間の正則埋め込み2009

    • Author(s)
      藤川英華
    • Organizer
      デーンセミナー
    • Place of Presentation
      東北大学
    • Year and Date
      2009-12-10
    • Related Report
      2010 Final Research Report
  • [Presentation] Infinite dimensional Teichmuller spaces and enlarged moduli spaces2009

    • Author(s)
      藤川英華
    • Organizer
      微分幾何・トポロジーセミナー
    • Place of Presentation
      慶応義塾大学
    • Year and Date
      2009-11-20
    • Related Report
      2010 Final Research Report
  • [Presentation] Dynamics of holomorphic self-embeddings of Teichmuller spaces2009

    • Author(s)
      藤川英華
    • Organizer
      XXIst Rolf Nevanlinna Colloquium
    • Place of Presentation
      京都大学
    • Year and Date
      2009-09-10
    • Related Report
      2009 Annual Research Report
  • [Presentation] Dynamics of holomorphic self-embeddings of Teichmuller spaces2009

    • Author(s)
      Ege Fujikawa
    • Organizer
      XXIst Rolf Nevanlinna Colloquium
    • Place of Presentation
      Kyoto University
    • Related Report
      2010 Final Research Report
  • [Presentation] 漸近的タイヒミュラーモジュラー群の楕円型元2008

    • Author(s)
      藤川英華
    • Organizer
      大阪大学低次元トポロジーセミナー
    • Place of Presentation
      大阪大学
    • Year and Date
      2008-10-28
    • Related Report
      2010 Final Research Report
  • [Presentation] Intermediate Teichmuller space : a moduli space for a Riemann surface of infinite type2008

    • Author(s)
      Ege Fujikawa
    • Organizer
      Hayama Symposium on Complex Analysis in Several Variables XII
    • Place of Presentation
      湘南国際村センター
    • Year and Date
      2008-07-14
    • Related Report
      2010 Final Research Report
  • [Presentation] 無限次元タイヒミュラー空間と複素解析的モジュライ空間の構造2008

    • Author(s)
      藤川英華
    • Organizer
      東大複素解析幾何セミナー
    • Place of Presentation
      東京大学
    • Year and Date
      2008-05-12
    • Related Report
      2010 Final Research Report
  • [Presentation] The Intermediate Teichmuller Spaces2008

    • Author(s)
      Ege Fujikawa
    • Organizer
      Complex Analysis and Dynamics Seminar
    • Place of Presentation
      City University of New York
    • Related Report
      2010 Final Research Report
  • [Presentation] Elliptic modular transformations on the Teichmuller and the asymptotic Teichmuller spaces2008

    • Author(s)
      Ege Fujikawa
    • Organizer
      Colloquium
    • Place of Presentation
      Wesleyan University
    • Related Report
      2010 Final Research Report
  • [Presentation] Periodicity of elliptic modular transformations on asymptotic Teichmuller spaces2008

    • Author(s)
      藤川英華
    • Organizer
      日本数学会2008年秋期総合分科会函数論分科会
    • Place of Presentation
      東京工業大学
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] Elliptic modular transformations on asymptotic Teichmuller spaces2008

    • Author(s)
      Ege Fujikawa
    • Organizer
      The 16th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Place of Presentation
      Dongguk University, Gyeongju, Korea
    • Related Report
      2010 Final Research Report
  • [Book] Infinite dimensional Teichmuller space and moduli space, RIMS Kokyuroku Bessatsu B172010

    • Author(s)
      Ege Fujikawa editor
    • Publisher
      Research Institute for Mathematical Sciences, Kyoto University
    • Related Report
      2010 Final Research Report
  • [Book] Infinite dimensional Teichmuller space and moduli space2010

    • Author(s)
      Ege Fujikawa
    • Total Pages
      133
    • Publisher
      Research Institute for Mathematical Sciences, Kyoto University
    • Related Report
      2010 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.math.s.chiba-u.ac.jp/~fujikawa/

    • Related Report
      2010 Final Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

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