威尼斯人娱乐场

Abstract

First, the concept of entropy in physics and geometry wil be discussed. In particular, Perelman’s W-entropy will bereviewed. Then the relation between entropy and Sobolev inequality and the uniform Sobolev inequality along the Ricci flow due to Rugang Ye will be presented. Some geometric applications such as in the case of Gromov almost flat manifolds will also be presented.