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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![Leo Sario [u.a.] Classification theory of Riemannian manifolds PDF](https://books.google.com/books/content/images/frontcover/KjOmtgAACAAJ?fife=w80-h100)
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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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: David Richeson
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 336
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Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea. From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V - E + F =2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.
Author: Louis Couturat
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 124
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