{"product_id":"isoperimetric-inequalities-differential-geometric-and-analytic-perspectives-paperback-9781107402270","title":"Isoperimetric Inequalities; Differential Geometric and Analytic Perspectives (Paperback \/ softback) 9781107402270","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eIsoperimetric Inequalities\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eDifferential Geometric and Analytic Perspectives\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eThis advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eIsaac Chavel (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781107402270, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 21 July 2011\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e282 pages\u003cbr\u003e22.9 x 15.2 x 1.6 cm, 0.42 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003eReview of the hardback: '[This book] constitues a valuable addition to the modern theory of inequalities.' Bulletin of the Belgian Mathematical Society\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis introduction treats the classical isoperimetric inequality in Euclidean space and contrasting rough inequalities in noncompact Riemannian manifolds. In Euclidean space the emphasis is on a most general form of the inequality sufficiently precise to characterize the case of equality, and in Riemannian manifolds the emphasis is on those qualitative features of the inequality which provide insight into the coarse geometry at infinity of Riemannian manifolds. The treatment in Euclidean space features a number of proofs of the classical inequality in increasing generality, providing in the process a transition from the methods of classical differential geometry to those of modern geometric measure theory; and the treatment in Riemannian manifolds features discretization techniques, and applications to upper bounds of large time heat diffusion in Riemannian manifolds. The result is an introduction to the rich tapestry of ideas and techniques of isoperimetric inequalities.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePart I. Introduction: 1. The isoperimetric problem\u003cbr\u003e 2. The isoperimetric inequality in the plane\u003cbr\u003e 3. Preliminaries\u003cbr\u003e 4. Bibliographic notes\u003cbr\u003e Part II. Differential Geometric Methods: 1. The C2 uniqueness theory\u003cbr\u003e 2. The C1 isoperimetric inequality\u003cbr\u003e 3. Bibliographic notes\u003cbr\u003e Part III. Minkowski Area and Perimeter: 1. The Hausdorff metric on compacta\u003cbr\u003e 2. Minkowski area and Steiner symmetrization\u003cbr\u003e 3. Application: the Faber-Krahn inequality\u003cbr\u003e 4. Perimeter\u003cbr\u003e 5. Bibliographic notes\u003cbr\u003e Part IV. Hausdorff Measure and Perimeter: 1. Hausdorff measure\u003cbr\u003e 2. The area formula for Lipschitz maps\u003cbr\u003e 3. Bibliographic notes\u003cbr\u003e Part V. Isoperimetric Constants: 1. Riemannian geometric preliminaries\u003cbr\u003e 2. Isoperimetric constants\u003cbr\u003e 3. Discretizations and isoperimetric inequalities\u003cbr\u003e 4. Bibliographic notes\u003cbr\u003e Part VI. Analytic Isoperimetric Inequalities: 1. L2-Sobolev inequalities\u003cbr\u003e 2. The compact case\u003cbr\u003e 3. Faber-Kahn inequalities\u003cbr\u003e 4. The Federer-Fleming theorem: the discrete case\u003cbr\u003e 5. Sobolev inequalities and discretizations\u003cbr\u003e 6. Bibliographic notes\u003cbr\u003e Part VII. Laplace and Heat Operators: 1. Self-adjoint operators and their semigroups\u003cbr\u003e 2. The Laplacian\u003cbr\u003e 3. The heat equation and its kernels\u003cbr\u003e 4. The action of the heat semigroup\u003cbr\u003e 5. Simplest examples\u003cbr\u003e 6. Bibliographic notes\u003cbr\u003e Part VIII. Large-Time Heat Diffusion: 1. The main problem\u003cbr\u003e 2. The Nash approach\u003cbr\u003e 3. The Varopoulos approach\u003cbr\u003e 4. Coulhon's modified Sobolev inequality\u003cbr\u003e 5. The denoument: geometric applications\u003cbr\u003e 6. Epilogue: the Faber–Kahn method\u003cbr\u003e 7. Bibliographic notes\u003cbr\u003e Bibliography.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Topology [\u003ca title=\"See our other books on Topology\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Topology%20%5BPBP%5D%22\"\u003ePBP\u003c\/a\u003e], 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], Calculus \u0026amp; mathematical analysis [\u003ca title=\"See our other books on Calculus \u0026amp; mathematical analysis\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Calculus%20\u0026amp;%20mathematical%20analysis%20%5BPBK%5D%22\"\u003ePBK\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":46265682526488,"sku":"9781107402270","price":46.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781107402270i.jpg?v=1694484827","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/isoperimetric-inequalities-differential-geometric-and-analytic-perspectives-paperback-9781107402270","provider":"Freshly Printed Books","version":"1.0","type":"link"}