
- 160 pages
- English
- PDF
- Available on iOS & Android
About this book
The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections “invariant metrics and pseudo-distances” and “hyperbolic complex manifolds” within the section “holomorphic mappings”. The invariant distance introduced in the first edition is now called the “Kobayashi distance”, and the hyperbolicity in the sense of this book is called the “Kobayashi hyperbolicity” to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.
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Table of contents
- CONTENTS
- Preface to the New Edition
- Preface
- Chapter I The Schwarz Lemma and Its Generalizations
- Chapter II Volume Elements and the Schwarz Lemma
- Chapter III Distance and the Schwarz Lemma
- Chapter IV Invariant Distances on Complex Manifolds
- Chapter V Holomorphic Mappings into Hyperbolic Manifolds
- Chapter VI The Big Picard Theorem and Extension of Holomorphic Mappings
- Chapter VII Generalization to Complex Spaces
- Chapter VIII Hyperbolic Manifolds and Minimal Models
- Chapter IX Miscellany
- Postscript
- Bibliography
- Summary of Notations
- Author Index
- Subject Index