作者：Translated by Otto F
页数：254页
出版社：世界图书出版公司
出版日期：1999
ISBN：9787506201117
电子书格式：pdf/epub/txt
内容简介
本书是Springer“数学研究生丛书”第81卷（GTM108），德文原版于1977年出版，是以作者在慕尼黑大学、明斯特大学讲课的讲义为基础写成的。
全书用现代分析观点简明扼要地论述了黎曼曲面的基本理论、最新成果和研究一维复变量所使用的各种方法。
作者简介
(德)Otto Forster，德国明斯特大学(Univerität München)数学系教授。明斯特大学始建于1631年，1945年以后，明斯特大学才开始发展到现今规模，成为德国最令人向往的学习地点之一。
目录
Preface
Chapter 1 Covering Spaces
1. The Definition of Riemann Surfaces
2. Elementary Properties of Holomorphic Mappings
3. Homotopy of Curves. The Fundamental Group
4. Branched and Unbranched Coverings
5. The Universal Covering and Covering Transformations
6. Sheaves
7. Analytic Continuation
8. Algebraic Functions
9. Differential Forms
10. The Integration of Differential Forms
11. Linear Differential Equations
Chapter 2 Compact Riemann Surfaces
12. Cohomology Groups
13. Dolbeault”s Lemma
14. A Finiteness Theorem
15. The Exact Cohomology Sequence
16. The Riemann-Roch Theorem
17. The Serre Duality Theorem
18. Functions and Differential Forms with Prescribed Principal Parts
19. Harmonic Differential Forms
20. Abel”s Theorem
21. The Jacobi Inversion Problem
Chapter 3 Non-compact Riemann Surfaces
22. The Dirichlet Boundary Value Problem
23. Countable Topology
24. Weyl’s Lemma
25. The Runge Approximation Theorem
26. The Theorems of Mittag-Leffler and Weierstrass
27. The Riemann Mapping Theorem
28. Functions with Prescribed Summands of Automorphy
29. Line and Vector Bundles
30. The Triviality of Vector Bundles
31. The Riemann-Hilbert Problem
Appendix
A. Partitions of Unity
B. Topological Vector Spaces
References
Symbol Index
Author and Subject Index
Chapter 1 Covering Spaces
1. The Definition of Riemann Surfaces
2. Elementary Properties of Holomorphic Mappings
3. Homotopy of Curves. The Fundamental Group
4. Branched and Unbranched Coverings
5. The Universal Covering and Covering Transformations
6. Sheaves
7. Analytic Continuation
8. Algebraic Functions
9. Differential Forms
10. The Integration of Differential Forms
11. Linear Differential Equations
Chapter 2 Compact Riemann Surfaces
12. Cohomology Groups
13. Dolbeault”s Lemma
14. A Finiteness Theorem
15. The Exact Cohomology Sequence
16. The Riemann-Roch Theorem
17. The Serre Duality Theorem
18. Functions and Differential Forms with Prescribed Principal Parts
19. Harmonic Differential Forms
20. Abel”s Theorem
21. The Jacobi Inversion Problem
Chapter 3 Non-compact Riemann Surfaces
22. The Dirichlet Boundary Value Problem
23. Countable Topology
24. Weyl’s Lemma
25. The Runge Approximation Theorem
26. The Theorems of Mittag-Leffler and Weierstrass
27. The Riemann Mapping Theorem
28. Functions with Prescribed Summands of Automorphy
29. Line and Vector Bundles
30. The Triviality of Vector Bundles
31. The Riemann-Hilbert Problem
Appendix
A. Partitions of Unity
B. Topological Vector Spaces
References
Symbol Index
Author and Subject Index
