Kleinian Groups and Uniformization in Examples and Problems

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American Mathematical Soc., Dec 31, 1986 - Mathematics - 198 pages
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Aimed at researchers, graduate students and undergraduates alike, this book presents a unified exposition of all the main areas and methods of the theory of Kleinian groups and the theory of uniformization of manifolds. The past 20 years have seen a rejuvenation of the field, due to the development of powerful new methods in topology, the theory of functions of several complex variables, and the theory of quasiconformal mappings. Thus this new book should provide a valuable resource, listing the basic facts regarding Kleinian groups and serving as a general guide to the primary literature, particularly the Russian literature in the field. In addition, the book includes a large number of examples, problems, and unsolved problems, many of them presented for the first time.
 

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Contents

General Properties of Kleinian Groups
1
Uniformization of Riemann Surfaces and Manifolds
27
Examples
63
Problems and Exercises further development of the theory
129
Some Unsolved Problems
171
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