Let M be a smooth connected manifold endowed with a smooth measure μ and a smooth locally subelliptic diffusion operator L which is symmetric with respect to μ. We assume that L satisfies a generalized curvature dimension inequality as introduced by Baudoin and Garofalo (2009) . Our goal is to discuss functional inequalities for μ like the Poincaré inequality, the log-Sobolev inequality or the Gaussian logarithmic isoperimetric inequality. © 2011 Elsevier Inc.
Baudoin, F., & Bonnefont, M. (2012). Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality. Journal of Functional Analysis, 262(6), 2646–2676. https://doi.org/10.1016/j.jfa.2011.12.020