Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds
Differential Geometry
2013-04-10 v2 Probability
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.
Keywords
Cite
@article{arxiv.1211.3778,
title = {Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds},
author = {Fabrice Baudoin and Jing Wang},
journal= {arXiv preprint arXiv:1211.3778},
year = {2013}
}
Comments
To appear in Potential Analysis