An Introduction to Teichmller Spaces [Paperback]

1 Teichm?ller Space of Genus g.- 1.1 Riemann Surfaces.- 1.2 Teichm?ller Space of Genus 1.- 1.3 Teichm?ller Space of Genus g.- 1.4 Quasiconformal Mappings and Teichm?ller Space.- 1.5 Complex Structures and Conformal Structures.- Notes.- 2 Frike Space.- 2.1 Uniformization Theorem.- 2.2 Universal Coverings.- 2.3 M?bius Transformations.- 2.4 Fuchsian Models.- 2.5 Fricke Space.- Notes.- 3 Hyperbolic Geometry and Fenchel-Nielsen Coordinates.- 3.1 Poincar? Metric and Hyperbolic Geometry.- 3.2 Fenchel-Nielsen Coordinates.- 3.3 Fricke-Klein Embedding.- 3.4 Thurstons Compactification.- Notes.- 4 Quasiconformal Mappings.- 4.1 Definitions and Elementary Properties.- 4.2 Existence Theorems on Quasiconformal Mappings.- 4.3 Dependence on Beltrami Coefficients.- 4.4 Proof of Calder?n-Zygmund Theorem.- Notes.- 5 Teichm?ller Spaces.- 5.1 Analytic Construction of Teichm?ller Spaces.- 5.2 Teichm?ller Mappings and Teichm?llers Theorerms.- 5.3 Proof of Teichm?llers Uniqueness Theorem.- Notes.- 6 Complex Analytic Theory of Teichm?ller Spaces.- 6.1 Bers Embedding.- 6.2 Invariance of Complex Structure of Teichm?ller Space.- 6.3 Teichm?ller Modular Groups.- 6.4 Roydens Theorems.- 6.5 Classification of Teichm?ller Modular Transformations.- Notes.- 7 Weil-Petersson Metric.- 7.1 Petersson Scalar Product and Bergman Projection.- 7.2 Infinitesimal Theory of Teichm?ller Spaces.- 7.3 Weil-Petersson Metric.- Notes.- 8 Fenchel-Nielsen Deformations and Weil-Petersson Metric.- 8.1 Fenchel-Nielsen Deformations.- 8.2 A Variational Formula for Geodesic Length Functions.- 8.3 Wolperts Formula.- Notes.- Appendices.- A Classical Variations on Riemann Surfaces.- Notes.- B Compactification of the Moduli Space.- Notes.- References.- List of Symbols.This introduction to the theory of Teichm?ller spaces will not only be used by graduate students and researchers in complex analysis and algebraic geometry, but also by theoretical physicists working with string theory. Starting with some basic facts on Riemannl£‰