| Description |
1 online resource (xiii, 279 pages 43 illustrations) |
| Contents |
1 Teichmüller Space of Genus g -- 1.1 Riemann Surfaces -- 1.2 Teichmüller Space of Genus 1 -- 1.3 Teichmüller Space of Genus g -- 1.4 Quasiconformal Mappings and Teichmüller Space -- 1.5 Complex Structures and Conformal Structures -- Notes -- 2 Frike Space -- 2.1 Uniformization Theorem -- 2.2 Universal Coverings -- 2.3 Möbius Transformations -- 2.4 Fuchsian Models -- 2.5 Fricke Space -- Notes -- 3 Hyperbolic Geometry and Fenchel-Nielsen Coordinates -- 3.1 Poincaré Metric and Hyperbolic Geometry -- 3.2 Fenchel-Nielsen Coordinates -- 3.3 Fricke-Klein Embedding -- 3.4 Thurston's 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 Calderón-Zygmund Theorem -- Notes -- 5 Teichmüller Spaces -- 5.1 Analytic Construction of Teichmüller Spaces -- 5.2 Teichmüller Mappings and Teichmüller's Theorerms -- 5.3 Proof of Teichmüller's Uniqueness Theorem -- Notes -- 6 Complex Analytic Theory of Teichmüller Spaces -- 6.1 Bers' Embedding -- 6.2 Invariance of Complex Structure of Teichmüller Space -- 6.3 Teichmüller Modular Groups -- 6.4 Royden's Theorems -- 6.5 Classification of Teichmüller Modular Transformations -- Notes -- 7 Weil-Petersson Metric -- 7.1 Petersson Scalar Product and Bergman Projection -- 7.2 Infinitesimal Theory of Teichmüller 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 Wolpert's Formula -- Notes -- Appendices -- A Classical Variations on Riemann Surfaces -- Notes -- B Compactification of the Moduli Space -- Notes -- References -- List of Symbols |
| Summary |
This book offers an easy and compact access to the theory of Teichmüller spaces, starting from the most elementary aspects to the most recent developments, e.g. the role this theory plays with regard to string theory. Teichmüller spaces give parametrization of all the complex structures on a given Riemann surface. This subject is related to many different areas of mathematics including complex analysis, algebraic geometry, differential geometry, topology in two and three dimensions, Kleinian and Fuchsian groups, automorphic forms, complex dynamics, and ergodic theory. Recently, Teichmüller spaces have begun to play an important role in string theory. Imayoshi and Taniguchi have attempted to make the book as self-contained as possible. They present numerous examples and heuristic arguments in order to help the reader grasp the ideas of Teichmüller theory. The book will be an excellent source of information for graduate students and researchers in complex analysis and algebraic geometry as well as for theoretical physicists working in quantum theory |
| Subject |
Mathematics.
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Geometry, Algebraic.
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Global analysis (Mathematics)
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Global differential geometry.
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Mathematics
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Geometry, Algebraic
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Global analysis (Mathematics)
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Global differential geometry
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Mathematics
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| Form |
Electronic book
|
| Author |
Taniguchi, Masahiko
|
| ISBN |
9784431681748 |
|
4431681744 |
|
