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

2012/11/16 by Fabrice Baudoin, Jing Wang, Baudoin, Fabrice +1 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.DG #math.PR

paper · pdf · doi:10.48550/arxiv.1211.3778

To appear in Potential Analysis

arxiv created 2013/04/09 · arxiv updated 2013/04/10

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.

Cited by

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

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