The logarithmic Sobolev inequality along the Ricci flow: the case $\lambda_0(g_0)=0$

TL;DR

This paper extends the understanding of the logarithmic Sobolev inequality along the Ricci flow to the case where the initial eigenvalue is zero, broadening the applicability of previous results.

Contribution

It generalizes previous work by establishing the inequality for initial conditions where bb_0(g_0)=0, filling a gap in the Ricci flow analysis.

Findings

Extended the logarithmic Sobolev inequality to bb_0(g_0)=0 case

Provided new insights into Ricci flow behavior with zero eigenvalue

Bridged the gap between positive and zero initial eigenvalue cases

Abstract

We extend our previous results on the logarithmic Sobolev inequality along the Ricci flow in the case $\lambda_0(g_0)>0$ to the case $\lambda_0(g_0)=0$.