Entropy Functionals, Sobolev Inequalities and kappa-Noncollapsing Estimates along the Ricci Flow
Abstract
Description
In this survey we review Hamilton's entropy and Perelman's entropy, and provide motivations for these concepts. Then we review recent results on the logarithmic Sobolev inequality, the Sobolev inequalities and kappa-noncollapsing estimates along the Ricci flow, including the Ricci flow with surgeries.
This survey was written for the 4th International Congress of Chinese Mathematicians to be held in Hangzhou, China in December 2007, and for the memorial volume dedicated to the 771 class of mathematics of China University of Science and Technology
This survey was written for the 4th International Congress of Chinese Mathematicians to be held in Hangzhou, China in December 2007, and for the memorial volume dedicated to the 771 class of mathematics of China University of Science and Technology