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黎曼曲面·第2版（英文版）

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作者：H.M.Farkas 著著

出版社：世界图书出版公司

出版时间：2003-9-1

I S B N：9787506259477

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黎曼曲面第2版

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黎曼曲面·第2版（英文版）

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黎曼曲面（第2版）

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内容简介

It is gratifying to learn that there is new life in an old field that has been at the center of one's existence for over a quarter of a century. It is particularly pleasing that the subject of Riemann surfaces has attracted the attention of a new generation of mathematicians from (newly) adjacent fields (for example, those interested in hyperbolic manifolds and iterations of rational maps) and young physicists who have been convinced (certainly not by mathematicians) that compact Riemann surfaces may play an important role in their (string) universe. We hope that non-mathematicians as well as mathematicians (working in nearby areas to the central topic of this book) will also learn part of this subject for the sheer beauty and elegance of the material (work of Weierstrass, Jacobi, Riemann, Hilbert, Weyl) and as healthy exposure to the way (some) mathematicians write about mathematics.

作者简介

Preface to the Second Edition
Preface to the First Edition
Commonly Used Symbols
CHAPTER 0 An Overview
0.1. Topological Aspects， Uniformization， and Fuchsian Groups
0.2. Algebraic Functions
0.3. Abelian Varieties
0.4. More Analytic Aspects
CHAPTER ⅠRiemann Surfaces
Ⅰ.1. Definitions and Examples
Ⅰ.2. Topology of Riemann Surfaces
Ⅰ.3. Differential Forms
Ⅰ.4. Integration Formulae
CHAPTER Ⅱ Existence Theorems
Ⅱ.1. Hilbert Space Theory--A Quick Review
Ⅱ.2. Weyl‘s Lemma
Ⅱ.3. The Hilbert Space of Square lntegrable Forms
Ⅱ.4.Harmonic Differentials
Ⅱ.5.Meromorphic Functions and Differentials
CHAPTER Ⅲ Compact Riemann Surfaces
CHAPTER Ⅳ Uniformization
CHAPTER Ⅴ Automorphisms of Compact Surfaces-Elementary Theory
CHAPTER Ⅵ Theta Functions
CHAPTER Ⅶ Exmples
Bibliography
Index