Advances in the Theory of Riemann Surfaces

by Lars Valerian Ahlfors, Lipman Bers

Overview

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.

Product Details

ISBN-13:	9780691080819
Publisher:	Princeton University Press
Publication date:	07/21/1971
Series:	Annals of Mathematics Studies , #66
Pages:	430
Product dimensions:	6.00(w) x 9.00(h) x (d)

Table of Contents

• Frontmatter, pg. i
• Preface, pg. v
• Contents, pg. vii
• Some Remarks on Kleinian Groups, pg. 1
• Vanishing Properties of Theta Functions for Abelian Covers of Riemann Surfaces, pg. 7
• Remarks on the Limit Point Set of a Finitely Generated Kleinian Group, pg. 19
• Extremal Quasiconformal Mappings, pg. 27
• Isomorphisms Between Teichmiiller Spaces, pg. 53
• On the Mapping Class Group of Closed Surfaces as Covering Spaces, pg. 81
• Schwarzian Derivatives and Mappings onto Jordan Domains, pg. 117
• On the Moduli of Closed Riemann Surfaces with Symmetries, pg. 119
• An Eigenvalue Problem for Riemann Surfaces, pg. 131
• Relations Between Quadratic Differentials, pg. 141
• Deformations of Embeddings of Riemann Surfaces in Projective Space, pg. 157
• Lipschitz Mappings and the p-capacity of Rings in n-space, pg. 175
• Spaces of Fuchsian Groups and Teichmülller Theory, pg. 195
• On Fricke Moduli, pg. 205
• Eichler Cohomology and the Structure of Finitely Generated Kleinian Groups, pg. 225
• On the Degeneration of Riemann Surfaces, pg. 265
• Singular Riemann Matrices, pg. 287
• An Inequality for Kleinian Groups, pg. 295
• On Klein's combination Theorem III, pg. 297
• On Finsler Geometry and Applications to Teichmilller Spaces, pg. 317
• Reproducing Formulas for Poincaré Series of Dimension -2 and Applications, pg. 329
• Period Relations on Riemann Surfaces, pg. 341
• Schottky Implies Poincaré, pg. 355
• Teichmülller Mappings which Keep the Boundary Pointwise Fixed, pg. 365
• Automorphisms and Isometries of Teichmilller Space, pg. 369
• Deformations of Embedded Riemann Surfaces, pg. 385
• Fock Representations and Theta-functions, pg. 393
• Uniforrnizations of Infinitely Connected Domains, pg. 407
• References, pg. 419