| Description |
1 online resource (x, 422 pages) |
| Contents |
Front cover; Preface; Contents; Chapter 1. Introduction; Chapter 2. Sobolev inequalities in the Euclidean space; Chapter 3. Basics of Riemann geometry; Chapter 4. Sobolev inquealities on manifolds and some consequences; Chapter 5. Basics of Ricci flow; Chapter 6. Perelman's entropies and Sobolev inequality for Ricci flow, the smooth case; Chapter 7. Properties of ancient k solutions and singularity analysis for 3-dimensional Ricci flow; Chapter 8. Sobolev inequality and the Ricci flow, the case with surgeries; Chapter 9. Applications to the proof of Poincare conjecture; Bibliography; Index |
| Summary |
Focusing on Sobolev inequalities and their applications to analysis on manifolds and Ricci flow, "Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincare Conjecture" introduces the field of analysis on Riemann manifolds and uses the tools of Sobolev imbedding and heat kernel estimates to study Ricci flows, especially with surgeries. The author explains key ideas, difficult proofs, and important applications in a succinct, accessible, and unified manner. The book first discusses Sobolev inequalities in various settings, including the Euclidean case, the Riemannian case |
| Bibliography |
Includes bibliographical references (pages 409-419) and index |
| Notes |
Print version record |
| Subject |
Inequalities (Mathematics)
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Poincaré conjecture.
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Ricci flow.
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Sobolev spaces.
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Inequalities (Mathematics)
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MATHEMATICS -- Algebra -- Elementary.
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Poincaré conjecture.
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Ricci flow.
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Sobolev spaces.
|
| Form |
Electronic book
|
| ISBN |
1282903098 |
|
1439834601 |
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9781282903098 |
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9781439834602 |
|
