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Author Zhang, Qi S.

Title Sobolev inequalities, heat kernels under Ricci flow, and the Poincaré conjecture / Qi S. Zhang
Published Boca Raton : CRC Press, ©2011
Online access available from:
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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)
Poincaré conjecture.
Ricci flow.
Sobolev spaces.
Inequalities (Mathematics)
MATHEMATICS -- Algebra -- Elementary.
Poincaré conjecture.
Ricci flow.
Sobolev spaces.
Form Electronic book
ISBN 1282903098