Hyperbolic Geometry from a Local Viewpoint (BOK)

Linda Keen, Nikola Lakic

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Written for graduate students, this book presents topics in 2-dimensional hyperbolic geometry. The authors begin with rigid motions in the plane which are used as motivation for a full development of hyperbolic geometry in the unit disk. The approach is to define metrics from an infinitesimal point of view; first the density is defined and then the metric via integration. The study of hyperbolic geometry in arbitrary domains requires the concepts of surfaces and covering spaces as well as uniformization and Fuchsian groups. These ideas are developed in the context of what is used later. The authors then provide a detailed discussion of hyperbolic geometry for arbitrary plane domains. New material on hyperbolic and hyperbolic-like metrics is presented. These are generalizations of the Kobayashi and Caratheodory metrics for plane domains. The book concludes with applications to holomorphic dynamics including new results and accessible open problems.

Produktfakta

Språk Engelsk Engelsk Innbinding Heftet
Utgitt 2007 Forfatter Linda Keen, Nikola Lakic
Forlag
CAMBRIDGE UNIVERSITY PRESS
ISBN 9780521682244
Antall sider 282 Dimensjoner 15,2cm x 22,8cm x 1,6cm
Vekt 402 gram Leverandør Bertram Trading Ltd
Emner og form Geometry