An Introduction to Teichmüller Spaces /

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Imayoshi, Yoichi
Otros Autores: Taniguchi, Masahiko
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Tokyo : Springer Japan, 1992.
Temas:
Mathematics.
Geometry, Algebraic.
Global analysis (Mathematics)
Global differential geometry.
Mathematics
Mathématiques.
Géométrie algébrique.
Analyse globale (Mathématiques)
Géométrie différentielle globale.
Geometry, Algebraic
Global differential geometry
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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