Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincare ConjectureCRC Press Fecha de publicación: 12/07/2010 Páginas: 432
Formato: Hardback 235 x 156 mm
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 Poincaré conjecture that clarifies and simplifies Perelman’s original proof.