Kleinian Groups and Uniformization in Examples and Problems
American Mathematical Soc., Dec 31, 1986 - Mathematics - 198 pages
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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Apanasov boundary circle closed Riemann surface compact complete hyperbolic conformal automorphisms conformal mapping conformal structure conformally equivalent conjugate consider constructed contains corresponding curve cyclic group defined degenerate groups Dehn surgery Denote diffeomorphism discrete group disk dodecahedron Euclidean example exists factor subgroup fi(G fiber Figure finite type finitely generated Kleinian fixed points free abelian free product Fuchsian group function fundamental group fundamental polygon fundamental polyhedron fundamental region fundamental set geometrically finite group G C Mn holomorphic homeomorphic homotopy hyperbolic manifold hyperbolic structure infinite invariant component isometric isometric spheres isomorphic Kleinian group knot Let G loops loxodromic manifold M(G Maskit Math metric Mobius mappings n-dimensional nontrivial obtained parabolic elements plane Poincare Problem Prove quasi-Fuchsian group quasicircles quasiconformal automorphism quasiconformal deformations quasiconformal mappings Schottky group set of discontinuity simply connected subgroup of G surface of genus Teichmiiller space three-dimensional manifold topological torsion-free torus transformations trivial uniformization
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