Hyperbolic Geometry from a Local Viewpoint by Linda Keen (English) Hardcover Boo

Description: Hyperbolic Geometry from a Local Viewpoint by Linda Keen, Nikola Lakic 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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. Notes 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. A detailed discussion of hyperbolic geometry for arbitrary plane domains is then given. New material on hyperbolic and hyperbolic-like metrics is presented, and the book concludes with applications to holomorphic dynamics including new results and accessible open problems. Author Biography 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. Table of Contents Introduction; 1. Elementary transformations; 2 Hyperbolic metric in the unit disk; 3. Holomorphic functions; 4. Topology and uniformization; 5. Discontinuous groups; 6 Fuchsian groups; 7. General hyperbolic metric; 8. The Kobayashi metric; 9. The Caratheodory pseudo metric; 10. Contraction properties; 11. Applications; 12 Applications II; 13. Applications III; 14. Estimating hyperbolic densities; 15. Uniformly perfect domains; 16 Appendix: Elliptic functions; Bibliography. Review 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 Review Quote 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 Promotional "Headline" A self-contained text on hyperbolic geometry for plane domains, ideal for graduate students and academic researchers. Description for Bookstore 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. Description for Library 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. Details ISBN0521863600 Author Nikola Lakic Short Title HYPERBOLIC GEOMETRY FROM A LOC Pages 271 Publisher Cambridge University Press Series London Mathematical Society Student Texts Language English ISBN-10 0521863600 ISBN-13 9780521863605 Media Book Format Hardcover DEWEY 516.9 Series Number 68 Illustrations Yes Year 2007 Publication Date 2007-03-31 Imprint Cambridge University Press Place of Publication Cambridge Country of Publication United Kingdom Edition 1st Residence Ashland, OR, US Birth 1947 Affiliation City University of New York DOI 10.1604/9780521863605 Audience Professional and Scholarly UK Release Date 2007-03-08 AU Release Date 2007-03-08 NZ Release Date 2007-03-08 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:168634736;

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