ENGLISH

Teichmüller Theory and Quadratic Differentials

By Frederick P. Gardiner

Book information

Publisher
Wiley-Interscience
Year
1987
ISBN
0471845396, 9780471845393
Language
english
Format
PDF
Filesize
11 MB (11100011 bytes)
Series
Pure and Applied Mathematics
Edition
1
Pages
256\238
DPI
600
Scanned
yes
Time added
2016-05-02 18:00:02
Language & Grammar;WritingReference;Almanacs & Yearbooks;Atlases & Maps;CareResearch & Publishing Guides;Calculus;Pure Mathema

Description

Offers a unified treatment of both the modern and the classical aspects of Teichmuller theory. The classical parts of the theory include Teichmuller's theorem on the existence and uniqueness of an extremal quasiconformal mapping in a given homotopy class of mappings between Riemann surfaces, the theorems of Bers and Ahlfors on the completeness of Poincare theta series for general Fuchsian groups and the approximation of integrable holomorphic functions in a domain by rational functions with simple poles on the boundary of the domain. The modern aspects of the theory include Ahlfors's and Bers's natural complex analytic coordinates for Teichmuller space, the infinitesimal theory of Teichmuller's metric and Kobayashi's metric, Royden's theorem that the only biholomorphic self-mappings of Teichmuller's space are induced by elements of the modular group (the action of which group is discontinuous), the Hamilton-Krushkal necessary condition for extremality, and Reich and Strebel's proof of sufficiency.

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