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.
Produktkennzeichnungen
ISBN-10
3642482716
ISBN-13
9783642482717
eBay Product ID (ePID)
194023222
Produkt Hauptmerkmale
Sprache
Englisch
Anzahl der Seiten
472 Seiten
Verlag
Springer Berlin Heidelberg, Springer Berlin
Publikationsname
Classification Theory of Riemann Surfaces
Autor
Mitsuru Nakai
Format
Taschenbuch
Erscheinungsjahr
2012
Zusätzliche Produkteigenschaften
Hörbuch
No
Inhaltsbeschreibung
Paperback
Item Length
23cm
Item Height
2cm
Item Width
15cm
Nummer Innerhalb der Serie
164
Mitautor
Leo Sario
Buchreihe
Grundlehren der Mathematischen Wissenschaften
Item Weight
709g
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