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Complex analytic geometry on the holomorphic branched covering structure

Research Project

Project/Area Number 19540181
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionNara Women's University

Principal Investigator

MASAHIKO Taniguchi (TANIGUCHI Masahiko)  Nara Women's University, 理学部, 教授 (50108974)

Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords複素解析 / 複素幾何 / 複素力学系 / 正則分岐被覆構造 / タイヒミュラー空間 / 国際情報交換 / アメリカ / アメリカ : 韓国 / アメリカ:韓国 / 多国籍
Research Abstract

The new geometrical compactification of the dynamical moduli space of polynomials is constructed, and also for the dynamical moduli space of rational functions, a natural system of global virtual coordinates is obtained. Next, a basic theory of the moduli spaces for holomorphic dynamics acting on the quasiconformal Teichmueller space is completely established, and furthermore as application, a fundamental theorem on the boundary behavior of holomorphic maps is proved.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (22 results)

All 2010 2009 2008 2007 Other

All Journal Article (18 results) (of which Peer Reviewed: 16 results) Presentation (3 results) Book (1 results)

  • [Journal Article] Stratification and coordinate systems for the moduli space of rational functions2010

    • Author(s)
      Masayo Fujimura, Masahiko Taniguchi
    • Journal Title

      Conf.Geom.and Dynam. 14

      Pages: 141-153

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Katsuhiko Matsuzaki, and Masahiko Taniguchi, Structure theorem for holomorphic self-covers and its appli cations2010

    • Author(s)
      Ege Fujikawa
    • Journal Title

      R.I.M.S.Kokyuroku Bessatsu B17

      Pages: 21-36

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Topological representation of the branched covering structure induced from a real rational function2010

    • Author(s)
      Mohaby Karima, Sayaka Tamae, Masahiko Taniguchi
    • Journal Title

      R.I.M.S.kokyuroku 1717

      Pages: 29-37

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stratification and coordinate systems for the moduli space of rational funotions2010

    • Author(s)
      Masayo Fujimura Masahiko Taniguchi
    • Journal Title

      Conf.Geom.and Dynam.

      Volume: 14 Pages: 141-153

    • 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

      R.I.M.S.Kokyuroku Bessatsu

      Volume: B17 Pages: 21-36

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dynamics of structurally finite entire functions with two singular values2009

    • Author(s)
      Shunsuke MorosawaK, Masahiko Taniguchi
    • Journal Title

      Comp.Meth.Funct.Th. 9

      Pages: 185-198

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dynamics of Structurally Finite Entire Functions with Two Singular Values2009

    • Author(s)
      Shunsuke Morosawa, Masahiko Taniguchi
    • Journal Title

      Comp.Meth.Funct.Th. 9

      Pages: 185-198

    • Related Report
      2009 Annual Research Report 2009 Self-evaluation Report
  • [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 2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A compactification of the moduli space of polynomials2008

    • Author(s)
      Masayo Fujimura, Masahiko Taniguchi
    • Journal Title

      Proc.Amer.Math.Soc. 136

      Pages: 3601-3609

    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] The moduli space of polynomials and its compactification2008

    • Author(s)
      Masayo Fujimura, Masahiko Taniguchi
    • Journal Title

      Complex Analysis and its Applications 1

      Pages: 175-178

    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A compactification of the moduli space of polynomials2008

    • Author(s)
      Masayo Fujimura
    • Journal Title

      Proc, Amer. Math. Soc. 136

      Pages: 3601-3609

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dynamics on Teichmuller spaces and self-covering of Riemann surfaces2008

    • Author(s)
      Ege Fujikawa
    • Journal Title

      Mathematische Zeitschrift 260

      Pages: 865-888

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The moduli space of polynomials and its compactification2008

    • Author(s)
      Masayo Fujimura and Masahiko Taniguchi
    • Journal Title

      Complex Analysis and its Applications 1

      Pages: 175-178

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Masahiko Taniguchi Equivalence problem for annuli and Bell representations in the plane2007

    • Author(s)
      Moonja Jeong, Jong-Won Oh
    • Journal Title

      Journal Math.Anal.Appl. 325

      Pages: 1295-1305

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Equivalence problem for annuli and Bell representations in the plane2007

    • Author(s)
      Moonja Jeong, Jong-Won Oh, Masahiko Taniguchi
    • Journal Title

      Journal Math.Anal.Appl. 325

      Pages: 1295-1305

    • Related Report
      2009 Self-evaluation Report
  • [Journal Article] Equivalence problem for annuli and Bell representations in the plane2007

    • Author(s)
      Moonja Jeong, Jong-Won Oh, and Masahiko Taniguchi
    • Journal Title

      Journal Math. Anal. Appl. 325

      Pages: 1295-1305

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Bell locus of rational functions and problems of Goldberg

    • Author(s)
      Masayo Fujimura, Mohaby Karima, Masahiko Taniguchi
    • Journal Title

      Comm.JSSAC(to appear)

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Bell locus of rational functions and problems of Goldberg

    • Author(s)
      Masayo Fujimura, Mohaby Karima, Masahiko Taniguchi
    • Journal Title

      Comm.JSSAC

      Volume: (To appear)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Degeneration of polynomial maps2008

    • Author(s)
      Masahiko Taniguchi
    • Organizer
      国際研究集会「Moduli and invariants in complex analysis and algebraic geometry」
    • Place of Presentation
      京都工芸繊維大学
    • Year and Date
      2008-11-26
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
  • [Presentation] Degeneration of polynomial maps2008

    • Author(s)
      Masahiko Taniguchi
    • Organizer
      Moduli and invariants in compex analy sis and algebraic geometry
    • Place of Presentation
      京都工芸繊維大学4号館
    • Year and Date
      2008-11-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] The moduli space of polynomials and its compactification2007

    • Author(s)
      Masayo Fujimura, Masahiko Taniguchi
    • Organizer
      15回FIDCA国際学会
    • Place of Presentation
      大阪市立大学学術情報総合センター
    • Year and Date
      2007-08-31
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report 2007 Annual Research Report
  • [Book] 数学辞典 第4版2007

    • Author(s)
      谷口雅彦, 他多数(日本数学会編集)
    • Total Pages
      1976
    • Publisher
      岩波書店
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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