2012/03/16 by Fabrice Baudoin, Baudoin, Fabrice, Bumsik Kim +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #math.DG #math.FA #math.PR
paper · pdf · doi:10.48550/arxiv.1203.3789
arxiv created 2012/03/16 · arxiv updated 2012/03/19
By adapting some ideas of M. Ledoux \citeledoux2, \citeledoux-stflour and \citeLed to a sub-Riemannian framework we study Sobolev, Poincaré and isoperimetric inequalities associated to subelliptic diffusion operators that satisfy the generalized curvature dimension inequality that was introduced by F. Baudoin and N. Garofalo in \citeBau2. Our results apply in particular on all CR Sasakian manifolds whose horizontal Webster-Tanaka-Ricci curvature is non negative, all Carnot groups with step two, and wide subclasses of principal bundles over Riemannian manifolds whose Ricci curvature is non negative.