Kleinian Groups and Uniformization in Examples and ProblemsAmerican Mathematical Soc., 1986/12/31 - 198 ページ 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. |
目次
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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多く使われている語句
Apanasov boundary circle closed Riemann surface compact complete hyperbolic conformal automorphisms conformal mapping conformal structure conformally equivalent conjugate consider constructed corresponding curve cyclic group defined degenerate groups Denote diffeomorphism discrete group disk dodecahedron elliptic Euclidean example exists factor subgroup fiber Figure finite type finitely generated Kleinian fixed points free product Fuchsian group function fundamental group fundamental polygon fundamental polyhedron fundamental region fundamental set G₁ G₂ geometrically finite group G C Mn holomorphic homeomorphic homotopy hyperbolic manifold hyperbolic structure infinite invariant component isometric isometric spheres isomorphic Kleinian group Let G loops loxodromic M₂ manifold M(G Maskit Math metric n-dimensional nontrivial obtained parabolic elements planar plane Poincaré polyhedra polyhedron problem Prove quasi-Fuchsian group quasiconformal deformations quasiconformal mappings Schottky group set of discontinuity simply connected subgroup of G surface of genus Teichmüller space three-dimensional manifold topological torsion-free torus transformations trivial uniformization
人気のある引用
183 ページ - MA Lavrent'ev, Variational methods for boundary value problems for systems of elliptic equations, Izdat.
184 ページ - Maclachlan, A bound for the number of automorphisms of a compact Riemann surface, J. London Math. Soc. 44 (1969) 265-272.
184 ページ - Lobacevskir space groups with an infinite fundamental region of finite measure. Dokl. Akad. Nauk SSSR 167 (1966), 30-33 = Soviet Math.
179 ページ - H. Garland and MS Raghunathan, Fundamental domains for lattices in (R-) rank 1 semisimple Lie groups, Ann. of Math. (2) 92 (1970), 279-326.
183 ページ - Geometrie der konformen Abbildung auf der hyperbolischen und der elliptischen Ebene, VEB Deutscher Verlag Wiss., Berlin, 1974.
187 ページ - Stallings, A topological proof of Grushko's theorem on free products, Math. Z. 90 (1965) 1-8.
179 ページ - Univalent functions and the Schwarzian derivative. Comment. Math. Helv. 52 (1977), 561-572.