Leo Sario

(Author)

Classification Theory of Riemann Surfaces (Softcover Reprint of the Original 1st 1970)Paperback - Softcover Reprint of the Original 1st 1970, 31 May 2012

Classification Theory of Riemann Surfaces (Softcover Reprint of the Original 1st 1970)
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Part of Series
Grundlehren Der Mathematischen Wissenschaften
Part of Series
Grundlehren Der Mathematischen Wissenschaften (Springer Hardcover)
Print Length
450 pages
Language
English
Publisher
Springer
Date Published
31 May 2012
ISBN-10
3642482716
ISBN-13
9783642482717

Description

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, SPEISER, TEICHMÜLLER and others obtaining incisive specific results. The main problem of finding necessary and sufficient conditions remains, however, unsolved.

Product Details

Authors:
Leo SarioMitsuru Nakai
Book Edition:
Softcover Reprint of the Original 1st 1970
Book Format:
Paperback
Country of Origin:
NL
Date Published:
31 May 2012
Dimensions:
23.39 x 15.6 x 2.41 cm
ISBN-10:
3642482716
ISBN-13:
9783642482717
Language:
English
Location:
Berlin, Heidelberg
Pages:
450
Publisher:
Weight:
653.17 gm

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