First variation of the Log Entropy functional along the Ricci flow

Abstract

In this note, we establish the first variation formula of the adjusted log entropy functional ${\mathcal{Y}}_a$ introduced by Ye in \cite{Y2}. As a direct consequence, we also obtain the monotonicity of ${\mathcal{Y}}_a$ along the Ricci flow.

4 pages. One remark improved

References in corpus (3)

• The logarithmic Sobolev inequality along the Ricci flow
• A uniform Sobolev inequality under Ricci flow
• Local gradient estimates of p-harmonic functions, 1/H-flow, and an entropy formula

Cited by in corpus (1)

• Ricci Flow and Entropy Model for Avascular Tumor Growth and Decay Control