Geometry of teichmüller spaces.

by Wong Chun-fai.Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.Includes bibliographical references (leaves 81-82).Chapter CHAPTER0 --- Introduction --- p.1Chapter CHAPTER1 --- Teichmuller Space of genus g --- p.5Chapter 1.1. --- Teichmiiller Space of genus gChapter 1.2. --- Fuchsian Model and Discrete subgroup of Aut(H)Chapter 1.3. --- Fricke SpaceChapter CHAPTER2 --- Hyperbolic Geometry and Fenchel-Nielsen Coordinates --- p.14Chapter 2.1. --- Poincare Metric and Hyperbolic GeometryChapter 2.2. --- Fenchel-Nielsen CoordinatesChapter 2.3. --- Fricke-Klein EmbeddingChapter CHAPTER3 --- Quasiconformal Mappings --- p.23Chapter 3.1. --- DefinitionsChapter 3.2. --- Existence Theorems on Quasiconformal MappingsChapter 3.3. --- Dependence on Beltrami CoefficientsChapter CHAPTER4 --- Teichmuller Spaces --- p.37Chapter 4.1. --- Analytic Construction of Teichmiiller SpacesChapter 4.2. --- Teichmiiller mapping and Teichmiiller TheoremChapter 4.3. --- Teichmiiller Uniqueness TheoremChapter CHAPTER5 --- Complex Analytic Theory of Teichmiiller Spaces --- p.50Chapter 5.1. --- Bers' Embedding and the complex structure of Teichmiiller SpaceChapter 5.2. --- Invariance of Complex Structure of Teichmiiller SpaceChapter 5.3. --- Teichmiiller Modular GroupsChapter 5.4. --- Classification of Teichmiiller Modular TransformationsChapter CHAPTER6 --- Weil-Petersson Metric --- p.68Chapter 6.1. --- Petersson Scalar Product and Reproducing formulaChapter 6.2. --- Infinitesimal Theory of Teichmuller SpacesChapter 6.3. --- Weil-Petersson MetricBIBLIOGRAPHY --- p.8