Hyperbolic geometry from a local viewpoint / / Linda Keen, Nikola Lakic [[electronic resource]]

• Autore: Keen Linda
• Pubblicazione: Cambridge : , : Cambridge University Press, , 2007
• Descrizione fisica: 1 online resource (x, 271 pages) : digital, PDF file(s)
• Disciplina: 516.9
• Soggetto topico: Geometry, Hyperbolic
• Persona (resp. second.): LakicNikola <1966->
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover; Series-title; Title; Copyright; Dedication; Contents; Introduction; 1 Elementary transformations of the Euclidean plane and the Riemann sphere; 2 Hyperbolic metric in the unit disk; 3 Holomorphic functions; 4 Topology and uniformization; 5 Discontinuous groups; 6 Fuchsian groups; 7 The hyperbolic metric for arbitrary domains; 8 The Kobayashi metric; 9 The Carathéodory pseudo-metric; 10 Inclusion mappings and contraction properties; 11 Applications I: forward random holomorphic iteration; 12 Applications II: backward random iteration; 13 Applications III: limit functions ; 14 Estimating hyperbolic densities15 Uniformly perfect domains; 16 Appendix: a brief survey of elliptic functions; Bibliography; Index
• Sommario/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.
• Titolo autorizzato: Hyperbolic geometry from a local viewpoint
• ISBN: 1-107-16900-3; 1-280-81565-5; 9786610815654; 0-511-27476-9; 0-511-27546-3; 0-511-27321-5; 0-511-32145-7; 0-511-61878-6; 0-511-27400-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910823642103321
• Lo trovi qui: Univ. Federico II
• Serie: London Mathematical Society student texts ; ; 68.