| 书目名称 | Classification Theory of Riemann Surfaces | | 编辑 | L. Sario,M. Nakai | | 视频video | http://file.papertrans.cn/228/227191/227191.mp4 | | 丛书名称 | Grundlehren der mathematischen Wissenschaften | | 图书封面 |  | | 描述 | The purpose of the present monograph is to systematically develop a classification theory of Riemann surfaces. Some first steps will also be taken toward a classification of Riemannian spaces. Four phases can be distinguished in the chronological background: the type problem; general classification; compactifications; and extension to higher dimensions. The type problem evolved in the following somewhat overlapping steps: the Riemann mapping theorem, the classical type problem, and the existence of Green‘s functions. The Riemann mapping theorem laid the foundation to classification theory: there are only two conformal equivalence classes of (noncompact) simply connected regions. Over half a century of efforts by leading mathematicians went into giving a rigorous proof of the theorem: RIEMANN, WEIERSTRASS, SCHWARZ, NEUMANN, POINCARE, HILBERT, WEYL, COURANT, OSGOOD, KOEBE, CARATHEODORY, MONTEL. The classical type problem was to determine whether a given simply connected covering surface of the plane is conformally equivalent to the plane or the disko The problem was in the center of interest in the thirties and early forties, with AHLFORS, KAKUTANI, KOBAYASHI, P. MYRBERG, NEVANLINNA, | | 出版日期 | Book 1970 | | 关键词 | Riemannsche Fläche; Surfaces; function; proof; theorem | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-48269-4 | | isbn_softcover | 978-3-642-48271-7 | | isbn_ebook | 978-3-642-48269-4Series ISSN 0072-7830 Series E-ISSN 2196-9701 | | issn_series | 0072-7830 | | copyright | Springer-Verlag Berlin 1970 |
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