Sobolev, Poincaré, and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality

摘要

By adapting some ideas of M. Ledoux cite{ledoux2}, cite{ledoux-stflour} andcite{Led} to a sub-Riemannian framework we study Sobolev, Poincar'e andisoperimetric inequalities associated to subelliptic diffusion operators thatsatisfy the generalized curvature dimension inequality that was introduced byF. Baudoin and N. Garofalo in cite{Bau2}. Our results apply in particular onall CR Sasakian manifolds whose horizontal Webster-Tanaka-Ricci curvature isnon negative, all Carnot groups with step two, and wide subclasses of principalbundles over Riemannian manifolds whose Ricci curvature is non negative.