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 $\\mu$\nand a smooth locally subelliptic diffusion operator $L$ which is symmetric with\nrespect to $\\mu$. We assume that $L$ satisfies a generalized curvature\ndimension inequality as introduced by Baudoin-Garofalo \\cite{BG1}. Our goal is\nto discuss functional inequalities for $\\mu$ like the Poincar\\'e inequality,\nthe log-Sobolev inequality or the Gaussian logarithmic isoperimetric\ninequality.\n