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arXiv · 1211.3778

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

Fabrice Baudoin·Jing Wang
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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.

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Fabrice Baudoin, Jing Wang. 2013-04-09. Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds. https://arxiv.org/abs/1211.3778

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