{"product_id":"harmonic-maps-between-riemannian-polyhedra-hardback-9780521773119","title":"Harmonic Maps between Riemannian Polyhedra (Hardback) 9780521773119","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eHarmonic Maps between Riemannian Polyhedra\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA research level book on harmonic maps between singular spaces, by renowned authors, first published in 2001.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJ. Eells (Author), B. Fuglede (Author), M. Gromov (Preface by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521773119, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 30 July 2001\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e312 pages\u003cbr\u003e22.9 x 15.2 x 2.1 cm, 0.63 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'This book can be highly recommended, both to specialists in the field, who will find a direct interest, and to geometers and analysts, who will find a source containing a large amount of material, with precise references. The organization of the chapters is excellent.' Luc Lemaire, Bulletin of the London Mathematical Society\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eHarmonic maps between smooth Riemannian manifolds play a ubiquitous role in differential geometry. Examples include geodesics viewed as maps, minimal surfaces, holomorphic maps and Abelian integrals viewed as maps to a circle. The theory of such maps has been extensively developed over the last 40 years, and has significant applications throughout mathematics. This 2001 book extends that theory in full detail to harmonic maps between broad classes of singular Riemannian polyhedra, with many examples being given. The analytical foundation is based on existence and regularity results which use the potential theory of Riemannian polyhedral domains viewed as Brelot harmonic spaces and geodesic space targets in the sense of Alexandrov and Busemann. The work sets out much material on harmonic maps between singular spaces and will hence serve as a concise source for all researchers working in related fields.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eGromov's preface\u003cbr\u003e Preface\u003cbr\u003e 1. Introduction\u003cbr\u003e Part I. Domains, Targets, Examples: 2. Harmonic spaces, Dirichlet spaces and geodesic spaces\u003cbr\u003e 3. Examples of domains and targets\u003cbr\u003e 4. Riemannian polyhedra\u003cbr\u003e Part II. Potential Theory on Polyhedra: 5. The Sobolev space W1,2(X). Weakly harmonic functions\u003cbr\u003e 6. Harnack inequality and Hölder continuity for weakly harmonic functions\u003cbr\u003e 7. Potential theory on Riemannian polyhedra\u003cbr\u003e 8. Examples of Riemannian polyhedra and related spaces\u003cbr\u003e Part III. Maps between Polyhedra: 9. Energy of maps\u003cbr\u003e 10. Hölder continuity of energy minimizers\u003cbr\u003e 11. Existence of energy minimizers\u003cbr\u003e 12. Harmonic maps - totally geodesic maps\u003cbr\u003e 13. Harmonic morphisms\u003cbr\u003e 14. Appendix A. Energy according to Korevaar-Schoen\u003cbr\u003e 15. Appendix B. Minimizers with small energy decay\u003cbr\u003e Bibliography\u003cbr\u003e Special symbols\u003cbr\u003e Index.\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":46265066488088,"sku":"9780521773119","price":98.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521773119i.jpg?v=1692019170","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/harmonic-maps-between-riemannian-polyhedra-hardback-9780521773119","provider":"Freshly Printed Books","version":"1.0","type":"link"}