Hyperbolic Geometry from a Local Viewpoint
Seiten
2007
Cambridge University Press (Verlag)
978-0-521-68224-4 (ISBN)
Cambridge University Press (Verlag)
978-0-521-68224-4 (ISBN)
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.
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.
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.
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.
| Erscheint lt. Verlag | 8.3.2007 |
|---|---|
| Reihe/Serie | London Mathematical Society Student Texts |
| Zusatzinfo | Worked examples or Exercises; 5 Halftones, unspecified; 27 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Gewicht | 402 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-521-68224-X / 052168224X |
| ISBN-13 | 978-0-521-68224-4 / 9780521682244 |
| Zustand | Neuware |
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