Hyperbolic Geometry from a Local Viewpoint - Brossura

Keen, Linda

Brossura

ISBN 10: 052168224X ISBN 13: 9780521682244

Casa editrice: Cambridge University Press, 2009

Riassunto

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.

Su questo libro

Recensione:

'Here new and interesting results are collected and presented for a target audience of graduate students and researchers, but the first half of the book is well accessible also for undergraduate students, and indeed everyone who is interested in an introduction to hyperbolic geometry.' Internationale Mathematische Nachrichten

Descrizione del libro:

Written for graduate students, this book presents topics in 2-dimensional hyperbolic geometry. The authors develop all the necessary basic theory, including the concepts of surfaces and covering spaces as well as uniformization and Fuchsian groups. Applications to holomorphic dynamics are discussed including new results and accessible open problems.

Su questa edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 2009
• ISBN 10: 052168224X
• ISBN 13: 9780521682244
• Rilegatura: Copertina flessibile
• Numero di pagine: 282