Riemann Surfaces pdf epub mobi txt 電子書下載2025

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出版者:Oxford University Press

作者:Simon Donaldson

出品人:

頁數:304

译者:

出版時間:2011-3-24

價格:USD 105.00

裝幀:Hardcover

isbn號碼:9780198526391

叢書系列:Oxford Graduate Texts in Mathematics

圖書標籤:

數學
Riemann麯麵
幾何
黎曼麵
Donalson
拓撲
分析
英國
數學
復分析
黎曼麯麵
代數幾何
拓撲學
復幾何
數學理論
高等數學
數學基礎
幾何學

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具體描述

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 connection with geometric topology, and in particular the role of the mapping class group, is also explained. To this end, some more sophisticated topics have been included, compared with traditional texts at this level. While the treatment is novel, the roots of the subject in traditional calculus and complex analysis are kept well in mind.

著者簡介

圖書目錄

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
· · · · · · (收起)

讀後感

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用戶評價

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不會

评分☆☆☆☆☆

讀完瞭前三部分

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一份現代黎曼麯麵講稿：解析開拓是黎曼麯麵理論最原始的齣發點；全純函數可以引齣代數方程和微分方程的解，serre duality是最為核心的分析定理：代替瞭調和函數和積分存在性證明工具----GUNIING。現代語言環路積分提供瞭一個局部解的解析開拓，沿麯綫解析延拓給瞭一個綫性映射; 投影空間討論仿射麯綫的漸進行為。關於黎曼羅赫定理最基礎的證明是建立在預知虧格和極點的基礎上 .

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非常好的復分析後續教程。本科階段看會受益匪淺。