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256: 2022/06/12(日)18:27 ID:Vf6rE6Wr(1/6) AAS
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複素解析学ホームページ
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名古屋大学大学院
多元数理科学研究科修士論文
省18
257(1): 2022/06/12(日)20:46 ID:Vf6rE6Wr(2/6) AAS
>>255
外部ﾘﾝｸ:en.wikipedia.org
Teichmuller space
It can be viewed as a moduli space for marked hyperbolic structure on the surface, and this endows it with a natural topology for which it is homeomorphic to a ball of dimension 6g-6 for a surface of genus g >= 2. In this way Teichmuller space can be viewed as the universal covering orbifold of the Riemann moduli space.
Contents
1 History
2 Definitions
省40
258: 2022/06/12(日)20:47 ID:Vf6rE6Wr(3/6) AAS
>>257
つづき
History
Moduli spaces for Riemann surfaces and related Fuchsian groups have been studied since the work of Bernhard Riemann (1826-1866), who knew that 6g-6 parameters were needed to describe the variations of complex structures on a surface of genus g >= 2. The early study of Teichmuller space, in the late nineteenth?early twentieth century, was geometric and founded on the interpretation of Riemann surfaces as hyperbolic surfaces. Among the main contributors were Felix Klein, Henri Poincare, Paul Koebe, Jakob Nielsen, Robert Fricke and Werner Fenchel.
The main contribution of Teichmuller to the study of moduli was the introduction of quasiconformal mappings to the subject. They allow us to give much more depth to the study of moduli spaces by endowing them with additional features that were not present in the previous, more elementary works. After World War II the subject was developed further in this analytic vein, in particular by Lars Ahlfors and Lipman Bers. The theory continues to be active, with numerous studies of the complex structure of Teichmuller space (introduced by Bers).
The geometric vein in the study of Teichmuller space was revived following the work of William Thurston in the late 1970s, who introduced a geometric compactification which he used in his study of the mapping class group of a surface. Other more combinatorial objects associated to this group (in particular the curve complex) have also been related to Teichmuller space, and this is a very active subject of research in geometric group theory.
(引用終り)
省1
259: 2022/06/12(日)23:01 ID:Vf6rE6Wr(4/6) AAS
擬等角写像 Quasiconformal mapping
外部ﾘﾝｸ:en.wikipedia.org
Quasiconformal mapping
Contents
1 Definition
2 A few facts about quasiconformal mappings
3 Measurable Riemann mapping theorem
省1
260: 2022/06/12(日)23:11 ID:Vf6rE6Wr(5/6) AAS
似ているが、ちょっと違う
Quasiregular map：between Euclidean spaces Rn of the same dimension or, more generally,・・
外部ﾘﾝｸ:en.wikipedia.org
Quasiregular map
In the mathematical field of analysis, quasiregular maps are a class of continuous maps between Euclidean spaces Rn of the same dimension or, more generally, between Riemannian manifolds of the same dimension, which share some of the basic properties with holomorphic functions of one complex variable.
Contents
1 Motivation
省4
261: 2022/06/12(日)23:24 ID:Vf6rE6Wr(6/6) AAS
Punctured Torus Group
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1998 Punctured Torus Groupに対するending lamination予想の解決（糸健太郎，小森洋平，須川敏幸，谷口雅彦）
目次・1-5章 PDF 1459KB 外部ﾘﾝｸ[pdf]:www.cajpn.org
6-9章 PDF 1452KB 外部ﾘﾝｸ[pdf]:www.cajpn.org
10-12章・参考文献 PDF 1546KB 外部ﾘﾝｸ[pdf]:www.cajpn.org
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