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