书名：Riemann Surfaces (Oxford Graduate Texts in Mathematics): 22 黎曼曲面 (牛津大学数学研究生教材)  

作者：imon Donaldson 

出版社名称：Oxford University Press, USA 

出版时间：2011 

语种：英语 

ISBN：9780199606740 

商品尺寸：.52 x 15.2 x 23.1 cm 

包装：平装 This clear and insightful text, from one of the foremost researchers in the field, is suitable for graduate or advanced undergraduate course on Riemann surfaces, and will provide fascinating reading for professional mathematicians. ― L'Enseignement Mathematique

An authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view; it pulls together material from global analysis, topology, and algebraic geometry, and covers the essential mathematical methods and tools.

Established author with an international research reputation

The topic stands at the centre of a number of key areas

Novel, innovative approach to the fundamental results

Emphasis on topology and the interaction with global analysis

一维复杂流形或黎曼曲面上的权威但可访问的文本。从多种角度处理黎曼曲面上的主要结果；它从全局分析，拓扑结构和代数几何学中收集材料，并涵盖了基本的数学方法和工具。

享誉国际的知名作家

该主题是许多关键领域的中心

新颖，创新的方法获得基本结果

强调拓扑结构以及与全局分析的交互作用

书籍目录

I Preliminaries

1:Holomorphic Functions

2:Surface Topology

II Basic Theory

3:Basic Definitions

4:Maps between Riemann Surfaces

5:Calculus on Surfaces

6:Elliptic functions and integrals

7:Applications of the Euler characteristic

III Deeper Theory

8:Meromorphic Functions and the Main Theorem for Compact Riemann Surfaces

9:Proof of the Main Theorem

10:The Uniformisation Theorem

IV Further Developments

11:Contrasts in Riemann Surface Theory

12:Divisors, Line Bundles and Jacobians

13:Moduli and Deformations

14:Mappings and Moduli

15:Ordinary Differential Equations

Bibliography

Index

Simon Donaldson gained a BA from Cambridge in 1979. In 1980 he began graduate work in Oxford, supervised by Nigel Hitchin and Sir Michael Atiyah. His PhD thesis studied mathematical aspects of Yang-Mills theory. In 1986, aged 29, he was awarded a Fields Medal and was elected to the Royal Society. He was Wallis Professor of Mathematics in Oxford between 1985 and 1998 when he moved to Imperial College London. Most of his work since has been on the interface between differential geometry and complex algebraic geometry. The recipient of numerous awards, including the Shaw Prize in 2009 with Clifford Taubes, he is also a Foreign Member of the US, French & Swedish academies. Donaldson has supervised more than 40 doctoral students, many of whom have gone on to become leading figures in research.