Advances in the Theory of Riemann Surfaces

Lars Valerian Ahlfors, Lipman Bers

• Publisher: Princeton University Press
• Year: 1971
• Print ISBN:
  9780691080819
• eBook ISBN:
  9781400822492
• Topic: Mathematics
• Subtopic: Calculus
• Index: Mathematics

Intended for researchers in Riemann surfaces, this volume summarizes a significant portion of the work done in the field during the years 1966 to 1971.

Table of contents

• Cover
• Title
• Copyright
• PREFACE
• CONTENTS
• Some Remarks On Kleinian Groups
• Vanishing Properties of Theta Functions for Abelian Covers of Riemann Surfaces
• Remarks on the Limit Point Set of a Finitely Generated Kleinian Group
• Extremal Quasiconformal Mappings
• Isomorphisms Between Teichmüller Spaces
• On the Mapping Class Group of Closed Surfaces as Covering Spaces
• Schwarzian Derivatives and Mappings onto Jordan Domains
• On the Moduli of Closed Riemann Surfaces with Symmetries
• An Eigenvalue Problem for Riemann Surfaces
• Relations Between Quadratic Differentials
• Deformations of Embeddings of Riemann Surfaces in Projective Space
• Lipschitz Mappings and the p-capacity of Rings in n-space
• Spaces of Fuchsian Groups and Teichmüller Theory
• On Fricke Moduli
• Eichler Cohomology and the Structure of Finitely Generated Kleinian Groups
• On the Degeneration of Riemann Surfaces
• Singular Riemann Matrices
• An Inequality for Kleinian Groups
• On Klein's combination Theorem III
• On Finsler Geometry and Applications to Teichmüller Spaces
• Reproducing Formulas for Poincaré Series of Dimension –2 and Applications
• Period Relations on Riemann Surfaces
• Schottky Implies Poincaré
• Teichmüller Mappings which Keep the Boundary Pointwise Fixed
• Automorphisms and Isometries of Teichmüller Space
• Deformations of Embedded Riemann Surfaces
• Fock Representations and Theta-functions
• Uniformizations of Infinitely Connected Domains