Riemann surfaces

Riemann surfaces

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作者: Simon Donaldson

出版社: Oxford University Press

出版时间: 2011-03

ISBN: 9780198526391

装帧: 精装

开本: 其他

纸张: 其他

分类: 外文古旧书>英文书>自然科学

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This graduate text on Riemann surface theory proves the fundamental analytical results on the existence of meromorphic functions and the Uniformisation Theorem. The approach taken emphasises PDE methods, applicable more generally in global analysis. The c 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
内容简介:
This graduate text on Riemann surface theory proves the fundamental analytical results on the existence of meromorphic functions and the Uniformisation Theorem. The approach taken emphasises PDE methods, applicable more generally in global analysis. The c
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

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