Curvature Dimension Inequalities and Subelliptic Heat Kernel Gradient Bounds on Contact Manifolds |
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Authors: | Fabrice Baudoin Jing Wang |
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Institution: | 1. Department of Mathematics, Purdue University, West Lafayette, IN, USA
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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: - 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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