Hyperbolic Geometry from a Local Viewpoint (Paperback)

Linda Keen

ISBN 10: 052168224X / ISBN 13: 9780521682244

Verlag: Cambridge University Press, Cambridge, 2007

Beschreibung

Paperback. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9780521682244

Bibliografische Details

Titel: Hyperbolic Geometry from a Local Viewpoint (...

Verlag: Cambridge University Press, Cambridge

Erscheinungsdatum: 2007

Einband: Paperback

Zustand: new

Auflage: 1. Auflage

Über diesen Titel

Inhaltsangabe:

A self-contained text on hyperbolic geometry for plane domains, ideal for graduate students and academic researchers.

Über die Autorinnen und Autoren:

Linda Keen is a Professor of Mathematics at the City University of New York, Lehman College and the Graduate Center.

Nikola Lakic is an Associate Professor of Mathematics at the City University of New York, Lehman College and the Graduate Center.