Monday, June 15, 2009

Hyperbolic Geometry from a Local Viewpoint (London Mathematical Society Student Texts)

Hyperbolic Geometry from a Local Viewpoint (London Mathematical Society Student Texts)

Hyperbolic Geometry from a Local Viewpoint (London Mathematical Society Student Texts) free ebook download.


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 asuniformization 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-likemetrics 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.

ISBN: 052168224X, Author: Linda Keen, Publisher: Cambridge University Press, Pages: 282, Publication Date: 2007-04-09


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