{"product_id":"hyperbolic-geometry-from-a-local-viewpoint-paperback-9780521682244","title":"Hyperbolic Geometry from a Local Viewpoint (Paperback) 9780521682244","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eHyperbolic Geometry from a Local Viewpoint\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA self-contained text on hyperbolic geometry for plane domains, ideal for graduate students  and academic researchers.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eLinda Keen (Author), Nikola Lakic (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521682244, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 8 March 2007\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e282 pages, 32 b\/w illus.  236 exercises\u003cbr\u003e22.9 x 15.2 x 1.6 cm, 0.402 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'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\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eWritten 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e 1. Elementary transformations\u003cbr\u003e 2 Hyperbolic metric in the unit disk\u003cbr\u003e 3. Holomorphic functions\u003cbr\u003e 4. Topology and uniformization\u003cbr\u003e 5. Discontinuous groups\u003cbr\u003e 6 Fuchsian groups\u003cbr\u003e 7. General hyperbolic metric\u003cbr\u003e 8. The Kobayashi metric\u003cbr\u003e 9. The Caratheodory pseudo metric\u003cbr\u003e 10. Contraction properties\u003cbr\u003e 11. Applications\u003cbr\u003e 12 Applications II\u003cbr\u003e 13. Applications III\u003cbr\u003e 14. Estimating hyperbolic densities\u003cbr\u003e 15. Uniformly perfect domains\u003cbr\u003e 16 Appendix: Elliptic functions\u003cbr\u003e Bibliography.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Geometry [\u003ca title=\"See our other books on Geometry\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Geometry%20%5BPBM%5D%22\"\u003ePBM\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46005445099800,"sku":"9780521682244","price":43.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521682244i_e8b12a2a-7b52-4942-bae5-6bf5c2f91f1a.jpg?v=1691379991","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/hyperbolic-geometry-from-a-local-viewpoint-paperback-9780521682244","provider":"Freshly Printed Books","version":"1.0","type":"link"}