Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds

Abstract

We study curvature dimension inequalities for the sub-Laplacian on contact Riemannian manifolds. This new curvature dimension condition is then used to obtain: 1) Geometric conditions ensuring the compactness of the underlying manifold (Bonnet-Myers type results); 2) Volume estimates of metric balls; 3) Gradient bounds and stochastic completeness for the heat semigroup generated by the sub-Laplacian; 4) Spectral gap estimates.

arXiv commentTo appear in Potential Analysis

References in corpus (1)

• A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality

Cited by in corpus (1)

• Poincare inequality and the uniqueness of solutions for the heat equation associated with subelliptic diffusion operators