Leo Sario [u.a.] Classification theory of Riemannian manifolds PDF Download
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Author: Theory
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Languages : en
Pages :
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Author: Theory
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Languages : en
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Author: Leo Sario
Publisher: Springer Science & Business Media
ISBN: 3642482694
Category : Mathematics
Languages : en
Pages : 469
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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.
Author: Leo Sario
Publisher: Lecture Notes in Mathematics
ISBN:
Category : Mathematics
Languages : en
Pages : 548
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Author: Lars Valerian Ahlfors
Publisher: Princeton University Press
ISBN: 140087453X
Category : Mathematics
Languages : en
Pages : 397
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The theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special character connected with the conformal structure, for instance: subharmonic, harmonic, and analytic functions. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 752
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Author: A. C. Schaeffer
Publisher: American Mathematical Soc.
ISBN: 1470429101
Category : Surfaces, Representation of
Languages : en
Pages : 330
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Book Description
Instead of investigating various isolated extremal problems in the theory of schlicht functions, the authors have concentrated their efforts on the investigation of the family of extremal schlicht functions in the large.
Author: Herman Chernoff
Publisher: SIAM
ISBN: 9781611970593
Category : Technology & Engineering
Languages : en
Pages : 124
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An exploration of the interrelated fields of design of experiments and sequential analysis with emphasis on the nature of theoretical statistics and how this relates to the philosophy and practice of statistics.
Author: Harish-Chandra
Publisher:
ISBN:
Category : Harmonic analysis
Languages : en
Pages : 40
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Author: Louis Couturat
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 124
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Book Description
Author: Anatoly A. Karatsuba
Publisher: Walter de Gruyter
ISBN: 3110886146
Category : Mathematics
Languages : en
Pages : 409
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Book Description
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
