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

Abstract

By adapting some ideas of M. Ledoux \cite{ledoux2}, \cite{ledoux-stflour} and \cite{Led} 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 \cite{Bau2}. 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.

References in corpus (2)

• A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality
• Bounds for the first eigenvalue of the horizontal Laplacian in positively curved sub-Riemannian manifolds

Cited by in corpus (3)

• Poincare inequality and the uniqueness of solutions for the heat equation associated with subelliptic diffusion operators
• An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence free torsion
• Heat kernel upper bounds under the generalized curvature(-dimension) inequality