Generalized Curvature Condition for Subelliptic Diffusion Processes

Abstract

By using a general version of curvature condition, derivative inequalities are established for a large class of subelliptic diffusion semigroups. As applications, the Harnack/cost-entropy/cost-variance inequalities for the diffusion semigroups, and the Poincaré/log-Sobolev inequalities for the associated Dirichlet forms in the symmetric case, are derived. Our results largely generalize and partly improve the corresponding ones obtained recently in [BB].

23 pages

References in corpus (2)

• On gradient bounds for the heat kernel on the Heisenberg group
• A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality

Cited by in corpus (7)

• Wasserstein contraction properties for hypoelliptic diffusions
• Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations, Part II
• Dimension free Harnack inequalities on $\RCD(K, \infty)$ spaces
• Convergence to equilibrium for hypoelliptic non-symmetric Ornstein-Uhlenbeck type operators
• Heat kernel upper bounds under the generalized curvature(-dimension) inequality
• Derivative Formulae and Poincaré Inequality for Kohn-Laplacian Type Semigroups
• A characterization of the rate of change of $\Phi$-entropy via an integral form curvature-dimension condition