Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality

Abstract

Let \(\M\) be a smooth connected manifold endowed with a smooth measure \(\mu\) and a smooth locally subelliptic diffusion operator \(L\) which is symmetric with respect to \(\mu\). We assume that \(L\) satisfies a generalized curvature dimension inequality as introduced by Baudoin-Garofalo \cite{BG1}. Our goal is to discuss functional inequalities for \(\mu\) like the Poincar\'e inequality, the log-Sobolev inequality or the Gaussian logarithmic isoperimetric inequality.