2000 Fiscal Year Annual Research Report

タイヒミュラー空間と写像類群の研究

Research Project

Project/Area Number	10440059
Research Institution	Osaka City University
Principal Investigator	今吉洋一大阪市立大学, 理学部, 教授 (30091656)
Co-Investigator(Kenkyū-buntansha)	佐官謙一大阪市立大学, 理学部, 助教授 (70110856) 河内明夫大阪市立大学, 理学部, 教授 (00112524) 加須栄篤大阪市立大学, 理学部, 教授 (40152657) 野口潤次郎東京大学, 大学院・数理科学研究科, 教授 (20033920) 小森洋平大阪市立大学, 理学部, 講師 (70264794)
Keywords	タイヒミュラー空間 / リーマン面 / クライン群 / 擬等角写像 / 写像類群 / タイヒミュラー・モデュラー群 / 正則写像 / 調和写像
Research Abstract	主に次の3つのテーマについて研究した。 1.リーマン面の正則族のモノドロミー群の元のタイプを、タイヒミュラー空間に作用する写像類群の観点からBers-Thurstonによる分類によって考察した。モノドロミー群、リーマン面の正則族の位相的な性質を表現するものであるが、その解析的な性質も強く規定するものである。本研究では特に、(1)小平曲面から自然に誘導される、リーマン面の正則族、および、(2)固定されたリーマン面R上の2点t_1,t_2,(t_1≠t_2)をパラメータとし、ファイバーがR＼{t_1,t_2}である。正則族の2つの場合のモノドロミー群の元のタイプを完全に決定することができた。 2.リーマン面の間の調和写像が正則になるための必要十分条件を求めた。それは「双曲型の閉リーマン面間の定数でない写像が正則、または反正則になるための必要十分条件はPoincare計量とBergman計量の両方に関して調和である」ことである。証明のアイディアは、調和写像の特徴付けを正則2次微分に関連させれことにある。 3.閉リーマン面の間の非定数正則写像の個数は高々有限個であると云うde Franchisの結果において、その個数を種数で評価できることを示した。証明には非定数正則写像のrigidity thoeremと非ユークリッド幾何の三角法(双曲三角法)を用いている。

Research Products
(21 results)

All Other

All Publications (21 results)

[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)
[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)
[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)
[Publications] Atsushi Kasue: "Convergence of Riemannian manifolds, Laplace operators and energy forms"Proc.of 5th. Pacific Rim Geometric Conference. (発表予定).
[Publications] Atsushi Kasue: "Convergence of Riemannian manifolds and Laplace operators ; I"Ann.Institut Fourier. (発表予定).
[Publications] Shin Kato: "Generic existence of minimal surfaces of genus gene with catenoidal ends and prescribed flux"Comm.Anal.Geom.. 8. 83-114 (2000)
[Publications] Taizo Kanenobu: "An unknotting operation on riffon 2-knots"J.Knot Theory Ramifications. 9. 1101-1028 (2000)
[Publications] Akio Kawauchi: "Floer homology of topological imitations of homology 3-spheres"J.Knot Theory Ramifications. 7. 41-60 (1998)
[Publications] Akio Kawauchi: "The quadratic form of link"Contemp.Math.. 233. 97-116 (1999)
[Publications] Ken-Ichi Sakan: "A conformal invariant dilation of quasisymmetry"Ann.Univ.Mariae Cuire-Sklodowska Sect.A. 53. 167-181 (1999)
[Publications] Yohei Komori: "The Riley slice revisited"Geometry and Topology Monographs. 1. 303-316 (1998)
[Publications] Masahiko Taniguchi: "A condition of quasi conformal extendability"Proc.Japan Acad.Ser.A.Math.Sci.. 75. 58-60 (1999)
[Publications] Masaharu Nishio: "A mean value property of poly-temperatures on a strip domain"J.Lodon Math.Soc (2). 58. 381-393 (1998)
[Publications] Masaharu Nishio: "Note on poly-supertemperatures and strip domain"Osaka J.Math.. 36. 539-556 (1999)
[Publications] Junjiro Noguchi: "The value distribution of holomorphic curves into semi-Abelian varieties"C.R.Acad.Sci.Pari,Seri I. 331. 235-240 (2000)
[Publications] Junjiro Noguchi: "On holomorphic curves in semi-Abelian varieties"Math.Z.. 228. 713-721 (1998)
[Publications] Fumio Maitani: "Conformal welding of annuli"Osaka J.Math.. 35. 579-591 (1998)
[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)
[Publications] Masahiko Taniguchi: "Holomorphic Dynamics"Cambridge Univ.Press. (1999)
[Publications] Masahiko Taniguchi: "Hyperbolic manifolds and Kleinian Groups"Oxford Univ.Press. (1998)
[Publications] Junichiro Noguchi: "Introduction to Complex Analysis"Amer.Math.Soc.. 250 (1997)

2000 Fiscal Year Annual Research Report

タイヒミュラー空間と写像類群の研究

Principal Investigator

今吉 洋一 大阪市立大学, 理学部, 教授 (30091656)

Research Products

[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)

[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)

[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)

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

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

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

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

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

[Publications] Akio Kawauchi: "The quadratic form of link"Contemp.Math.. 233. 97-116 (1999)

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

[Publications] Yohei Komori: "The Riley slice revisited"Geometry and Topology Monographs. 1. 303-316 (1998)

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

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

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

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

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

[Publications] Fumio Maitani: "Conformal welding of annuli"Osaka J.Math.. 35. 579-591 (1998)

[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)

[Publications] Masahiko Taniguchi: "Holomorphic Dynamics"Cambridge Univ.Press. (1999)

[Publications] Masahiko Taniguchi: "Hyperbolic manifolds and Kleinian Groups"Oxford Univ.Press. (1998)

[Publications] Junichiro Noguchi: "Introduction to Complex Analysis"Amer.Math.Soc.. 250 (1997)

今吉洋一大阪市立大学, 理学部, 教授 (30091656)