| 书目名称 | Complex Analysis, Riemann Surfaces and Integrable Systems | | 编辑 | Sergey M. Natanzon | | 视频video | http://file.papertrans.cn/232/231391/231391.mp4 | | 概述 | Using basic tools from the first year of university studies, the book leads a reader to the impressive achievements of mathematics of the 21st century.Studying the book, the reader will get acquainted | | 丛书名称 | Moscow Lectures | | 图书封面 |  | | 描述 | .This book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided. ..We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contracted space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We also construct theta functions that are very important for a range of applications. ..After that, we turn to modern applications of this theory. First, we build the (important for mathematics and mathematical physics) Kadomtsev-Petviashvili hierarchy and use validated results to arrive at important solutions to these differential equations. We subsequently use the theory of harmonic functions and the theory of differential hierarchies to explicitly construct a conformal mapping that translates an arbitrary contractible domain into a standard disk | | 出版日期 | Textbook 2019 | | 关键词 | meromorphic functions; Riemann theorem; harmonic functions; Fuchsian groups; Riemann surfaces; moduli of | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-34640-9 | | isbn_softcover | 978-3-030-34642-3 | | isbn_ebook | 978-3-030-34640-9Series ISSN 2522-0314 Series E-ISSN 2522-0322 | | issn_series | 2522-0314 | | copyright | Springer Nature Switzerland AG 2019 |
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