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.
發表於2024-10-31
Riemann Surfaces 2024 pdf epub mobi 電子書 下載
圖書標籤: 數學 Riemann麯麵 幾何 黎曼麵 Donalson 拓撲 分析 英國
讀完瞭前三部分
評分讀完瞭前三部分
評分非常好的復分析後續教程。本科階段看會受益匪淺。
評分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 .
評分讀完瞭前三部分
Riemann Surfaces 2024 pdf epub mobi 電子書 下載