Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives: Cambridge Tracts in Mathematics, cartea 145
Autor Isaac Chavelen Limba Engleză Paperback – 20 iul 2011
Toate formatele și edițiile | Preț | Express |
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Paperback (1) | 443.11 lei 6-8 săpt. | |
Cambridge University Press – 20 iul 2011 | 443.11 lei 6-8 săpt. | |
Hardback (1) | 789.51 lei 6-8 săpt. | |
Cambridge University Press – 22 iul 2001 | 789.51 lei 6-8 săpt. |
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Specificații
ISBN-13: 9781107402270
ISBN-10: 1107402271
Pagini: 282
Dimensiuni: 152 x 229 x 16 mm
Greutate: 0.42 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Tracts in Mathematics
Locul publicării:New York, United States
ISBN-10: 1107402271
Pagini: 282
Dimensiuni: 152 x 229 x 16 mm
Greutate: 0.42 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Tracts in Mathematics
Locul publicării:New York, United States
Cuprins
Part I. Introduction: 1. The isoperimetric problem; 2. The isoperimetric inequality in the plane; 3. Preliminaries; 4. Bibliographic notes; Part II. Differential Geometric Methods: 1. The C2 uniqueness theory; 2. The C1 isoperimetric inequality; 3. Bibliographic notes; Part III. Minkowski Area and Perimeter: 1. The Hausdorff metric on compacta; 2. Minkowski area and Steiner symmetrization; 3. Application: the Faber-Krahn inequality; 4. Perimeter; 5. Bibliographic notes; Part IV. Hausdorff Measure and Perimeter: 1. Hausdorff measure; 2. The area formula for Lipschitz maps; 3. Bibliographic notes; Part V. Isoperimetric Constants: 1. Riemannian geometric preliminaries; 2. Isoperimetric constants; 3. Discretizations and isoperimetric inequalities; 4. Bibliographic notes; Part VI. Analytic Isoperimetric Inequalities: 1. L2-Sobolev inequalities; 2. The compact case; 3. Faber-Kahn inequalities; 4. The Federer-Fleming theorem: the discrete case; 5. Sobolev inequalities and discretizations; 6. Bibliographic notes; Part VII. Laplace and Heat Operators: 1. Self-adjoint operators and their semigroups; 2. The Laplacian; 3. The heat equation and its kernels; 4. The action of the heat semigroup; 5. Simplest examples; 6. Bibliographic notes; Part VIII. Large-Time Heat Diffusion: 1. The main problem; 2. The Nash approach; 3. The Varopoulos approach; 4. Coulhon's modified Sobolev inequality; 5. The denoument: geometric applications; 6. Epilogue: the Faber–Kahn method; 7. Bibliographic notes; Bibliography.
Recenzii
Review of the hardback: 'The presentation of the book is clear and elegant, and gives expression to the beauty of the subject. It is a great pleasure to read this book, which is a profound source text for both classical and modern methods, and which will be equally valuable to graduate students and researchers in analysis and geometry.' Bulletin of the London Mathematical Society
Review of the hardback: 'The book is very useful in two ways. First, it nicely explains the story of the classical isoperimetric inequality, a result with a big disproportion between the ease of formulation and difficulty of the proof. This second part contains deep results obtained by the author.' European Mathematical Society
Review of the hardback: '… very useful …' EMS Newsletter
Review of the hardback: '[This book] constitues a valuable addition to the modern theory of inequalities.' Bulletin of the Belgian Mathematical Society
Review of the hardback: 'The book is very useful in two ways. First, it nicely explains the story of the classical isoperimetric inequality, a result with a big disproportion between the ease of formulation and difficulty of the proof. This second part contains deep results obtained by the author.' European Mathematical Society
Review of the hardback: '… very useful …' EMS Newsletter
Review of the hardback: '[This book] constitues a valuable addition to the modern theory of inequalities.' Bulletin of the Belgian Mathematical Society
Descriere
This advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject.