Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincare Conjecture - Zhang, Qi S.

Focusing on Sobolev inequalities and their applications to analysis on manifolds and Ricci flow, this title 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.