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Hyperbolic Geometry from a Local Viewpoint (London Mathematical Society Student Texts, Series Number 68) - Softcover
Synopsis
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.
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Book Description
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.
About the Author
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.
"About this title" may belong to another edition of this title.
- PublisherCambridge University Press
- Publication date2007
- ISBN 10 052168224X
- ISBN 13 9780521682244
- BindingPaperback
- LanguageEnglish
- Edition number1
- Number of pages282
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Hyperbolic Geometry from a Local Viewpoint (London Mathematical Society Student Texts, Series Number 68)
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ISBN 13: 9780521682244
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London Mathematical Society Student Texts: Hyperbolic Geometry from a Local Viewpoint (Volume 68)
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ISBN 10: 052168224X
ISBN 13: 9780521682244
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Hyperbolic Geometry from a Local Viewpoint: 68 (London Mathematical Society Student Texts, Series Number 68)
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Hyperbolic Geometry from a Local Viewpoint: 68 (London Mathematical Society Student Texts, Series Number 68)
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Hyperbolic Geometry from a Local Viewpoint (London Mathematical Society Student Texts, Series Number 68)
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Hyperbolic Geometry from a Local Viewpoint (Paperback)
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Paperback. Condition: new. 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. Seller Inventory # 9780521682244
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