Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincare Conjecture

By Qi S. Zhang

This book introduces the field of analysis on Riemann manifolds and uses the tools of Sobolev imbedding and heat kernel estimates to study Ricci flows with surgeries. It first discusses Sobolev inequalities in various settings, including the Euclidean case, the Riemannian case, and the Ricci flow case. The text then explores several applications and ramifications, such as heat kernel estimates, Perelman's W entropies and Sobolev inequality with surgeries, and the proof of Hamilton's little loop conjecture with surgeries. Using these tools, the author presents a unified approach to the Poincar conjecture that clarifies and simplifies Perelman's original proof.

• Format: Hardcover
• Language: English
• ISBN: 1439834598
• ISBN13: 9781439834596
• Release Date: July 2010
• Publisher: CRC Press
• Length: 432 Pages
• Weight: 1.65 lbs.
• Dimensions: 1.1" x 6.2" x 9.4"