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Classification Theory of Riemann Surfaces by Leo Sario, Mitsuru Nakai - Paperback
453.60 AED

Classification Theory of Riemann Surfaces by Leo Sario, Mitsuru Nakai - Paperback

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Category Type
Mathematics
ISBN
9783642482717
Author
Leo Sario, Mitsuru Nakai
Publisher
Springer
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 ...

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    Specifications

    Category Type
    Mathematics
    ISBN
    9783642482717
    Languages
    English
    Item EAN
    2724437258053
    People
    Author
    Leo Sario, Mitsuru Nakai
    Category Type
    Mathematics
    ISBN
    9783642482717
    Languages
    English
    Item EAN
    2724437258053
    People
    Author
    Leo Sario, Mitsuru Nakai
    People
    Publisher
    Springer
    Technical Information
    Binding
    Paperback
    Languages and countries
    Book Language
    English
    Read more
  •  

    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

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

    Product Features:
    • Category: Mathematics
    • Binding: Paperback
    • Language of Text: English
    • Author(s): Leo Sario, Mitsuru Nakai
    • Publisher: Springer
    • ISBN: 9783642482717
    • Number of Pages: 450
    • Dimensions: 9.21 x 6.14 x 0.95 inches
 

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