Complex analytic geometry on the holomorphic branched covering structure

• Project/Area Number: 19540181
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Nara 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: ¥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.

Research Products

• [Journal Article] Stratification and coordinate systems for the moduli space of rational functions (2010)
  • Author(s): Masayo Fujimura, Masahiko Taniguchi
  • Journal Title: Conf.Geom.and Dynam. 14 Pages: 141-153
  • Peer Reviewed
• [Journal Article] Katsuhiko Matsuzaki, and Masahiko Taniguchi, Structure theorem for holomorphic self-covers and its appli cations (2010)
  • Author(s): Ege Fujikawa
  • Journal Title: R.I.M.S.Kokyuroku Bessatsu B17 Pages: 21-36
  • Peer Reviewed
• [Journal Article] Topological representation of the branched covering structure induced from a real rational function (2010)
  • Author(s): Mohaby Karima, Sayaka Tamae, Masahiko Taniguchi
  • Journal Title: R.I.M.S.kokyuroku 1717 Pages: 29-37
  • Peer Reviewed
• [Journal Article] Stratification and coordinate systems for the moduli space of rational funotions (2010)
  • Author(s): Masayo Fujimura Masahiko Taniguchi
  • Journal Title: Conf.Geom.and Dynam. Volume: 14 Pages: 141-153
  • Peer Reviewed
• [Journal Article] Structure theorem for holomorphic self-covers and its applications (2010)
  • Author(s): Ege Fujikawa, Katsuhiko Matsuzaki, Masahiko Taniguchi
  • Journal Title: R.I.M.S.Kokyuroku Bessatsu Volume: B17 Pages: 21-36
  • Peer Reviewed
• [Journal Article] Dynamics of structurally finite entire functions with two singular values (2009)
  • Author(s): Shunsuke MorosawaK, Masahiko Taniguchi
  • Journal Title: Comp.Meth.Funct.Th. 9 Pages: 185-198
  • Peer Reviewed
• [Journal Article] Dynamics of Structurally Finite Entire Functions with Two Singular Values (2009)
  • Author(s): Shunsuke Morosawa, Masahiko Taniguchi
  • Journal Title: Comp.Meth.Funct.Th. 9 Pages: 185-198
• [Journal Article] Dynamics on Teichmuller spaces and self-covering of Riemann surfaces (2008)
  • Author(s): Ege Fujikawa, Katsuhiko Matsuzaki, Masahiko Taniguchi
  • Journal Title: Mathematische Zeitschrift 260 Pages: 865-888
  • Peer Reviewed
• [Journal Article] A compactification of the moduli space of polynomials (2008)
  • Author(s): Masayo Fujimura, Masahiko Taniguchi
  • Journal Title: Proc.Amer.Math.Soc. 136 Pages: 3601-3609
  • Peer Reviewed
• [Journal Article] The moduli space of polynomials and its compactification (2008)
  • Author(s): Masayo Fujimura, Masahiko Taniguchi
  • Journal Title: Complex Analysis and its Applications 1 Pages: 175-178
  • Peer Reviewed
• [Journal Article] A compactification of the moduli space of polynomials (2008)
  • Author(s): Masayo Fujimura
  • Journal Title: Proc, Amer. Math. Soc. 136 Pages: 3601-3609
  • Peer Reviewed
• [Journal Article] Dynamics on Teichmuller spaces and self-covering of Riemann surfaces (2008)
  • Author(s): Ege Fujikawa
  • Journal Title: Mathematische Zeitschrift 260 Pages: 865-888
  • Peer Reviewed
• [Journal Article] The moduli space of polynomials and its compactification (2008)
  • Author(s): Masayo Fujimura and Masahiko Taniguchi
  • Journal Title: Complex Analysis and its Applications 1 Pages: 175-178
  • Peer Reviewed
• [Journal Article] Masahiko Taniguchi Equivalence problem for annuli and Bell representations in the plane (2007)
  • Author(s): Moonja Jeong, Jong-Won Oh
  • Journal Title: Journal Math.Anal.Appl. 325 Pages: 1295-1305
  • Peer Reviewed
• [Journal Article] Equivalence problem for annuli and Bell representations in the plane (2007)
  • Author(s): Moonja Jeong, Jong-Won Oh, Masahiko Taniguchi
  • Journal Title: Journal Math.Anal.Appl. 325 Pages: 1295-1305
• [Journal Article] Equivalence problem for annuli and Bell representations in the plane (2007)
  • Author(s): Moonja Jeong, Jong-Won Oh, and Masahiko Taniguchi
  • Journal Title: Journal Math. Anal. Appl. 325 Pages: 1295-1305
  • 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)
  • 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)
  • Peer Reviewed
• [Presentation] Degeneration of polynomial maps (2008)
  • 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
• [Presentation] Degeneration of polynomial maps (2008)
  • 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
• [Presentation] The moduli space of polynomials and its compactification (2007)
  • 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
• [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