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The Geometric Theory of Complex Variables

This book provides the reader with a broad introduction to the geometric methodology in complex analysis. It covers both single and several complex variables, creating a dialogue between the two viewpoints. Regarded as one of the 'grand old ladies' of modern mathematics, complex analysis t...

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Detalles Bibliográficos
Autores principales: Dovbush, Peter V. (Autor), Krantz, Steven G. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Lenguaje:inglés
Publicado: Cham : Springer Nature Switzerland : Imprint: Springer, 2025.
Edición:1st ed. 2025.
Materias:
Global analysis (Mathematics).
Manifolds (Mathematics).
Functions of complex variables.
Functional analysis.
Global Analysis and Analysis on Manifolds.
Several Complex Variables and Analytic Spaces.
Functional Analysis.
Acceso en línea:https://doi.org/10.1007/978-3-031-77204-7
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Tabla de Contenidos:
  • - Introduction
  • The Riemann Mapping Theorem
  • The Ahlfors Map
  • A Riemann Mapping Theorem for Two-Connected Domains in the Plane
  • Riemann Multiply Connected Domains
  • Quasiconformal Mappings
  • Manifolds
  • Riemann Surfaces
  • The Uniformization Theorem
  • Automorphism Groups
  • Ridigity of Holomorphic Mappings and a New Schwarz Lemma at the Boundary
  • The Schwarz Lemma and Its Generalizations
  • Invariant Distances on Complex Manifolds
  • Hyperbolic Manifolds
  • The Fatou Theory and Related Matters
  • The Theorem of Bun Wong and Rosay
  • Smoothness to the Boundary of Biholomorphic Mappings
  • Solution ∂ problem
  • Harmonic measure
  • Quadrature
  • Teichmüller Theory
  • Bibliography
  • Index.

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