Hyperbolic Menifolds and Kleinian Groups

ISBN-13: 9780198500629 / Angielski / Twarda / 1998 / 264 str.

Katsuhiko Matsuzaki; Masahiko Taniguchi

Opis

A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space, which is also regarded as a subgroup of Mobius transformations in the complex plane. The present book is a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry and complex analysis. After 1960, Ahlfors and Bers produced important work which helped make Kleinian groups an active area of complex analysis as a branch of Teichmuller theory. Later, Thurston brought about a revolution in the field with his profound investigation of hyperbolic manifolds, and Sullivan developed an important complex dynamical approach. This book provides the fundamental results and key theorems necessary for access to the frontiers of the theory from a modern viewpoint.
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Recenzje

'The presentation of the whole theory is very nice...the book reads well, and will be interesting and accessible for mathematicians from several branches of mathematics' EMS