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Sobolev inequalities, heat kernels under Ricci flow, and the Poincaré conjecture /

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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...

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Bibliographic Details
Main Author: Zhang, Qi S. (Author)
Corporate Author: Taylor & Francis
Format: eBook
Language:English
Published: Boca Raton : CRC Press, [2011].
Subjects:
Inequalities (Mathematics)
Sobolev spaces.
Ricci flow.
Poincaré conjecture.
Inégalités (Mathématiques)
Espaces de Sobolev.
Flot de Ricci.
Conjecture de Poincaré.
MATHEMATICS > Algebra > Elementary.
Poincaré conjecture
Ricci flow
Sobolev spaces
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of 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.