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Cover: 9780521682244 | Hyperbolic Geometry from a Local Viewpoint | Linda Keen (u. a.) | Buch
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Hyperbolic Geometry from a Local Viewpoint
Taschenbuch von Linda Keen (u. a.)
Sprache: Englisch

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Beschreibung
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.
Über den Autor
Linda Keen is a Professor of Mathematics at the City University of New York, Lehman College and the Graduate Center.
Zusammenfassung
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.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2007
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9780521682244
ISBN-10: 052168224X
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Keen, Linda
Lakic, Nikola
Hersteller: Cambridge University Press
Maße: 229 x 152 x 17 mm
Von/Mit: Linda Keen (u. a.)
Erscheinungsdatum: 08.03.2007
Gewicht: 0,462 kg
Artikel-ID: 102064326
Über den Autor
Linda Keen is a Professor of Mathematics at the City University of New York, Lehman College and the Graduate Center.
Zusammenfassung
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.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2007
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9780521682244
ISBN-10: 052168224X
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Keen, Linda
Lakic, Nikola
Hersteller: Cambridge University Press
Maße: 229 x 152 x 17 mm
Von/Mit: Linda Keen (u. a.)
Erscheinungsdatum: 08.03.2007
Gewicht: 0,462 kg
Artikel-ID: 102064326
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