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Curvature Dimension Inequalities and Subelliptic Heat Kernel Gradient Bounds on Contact Manifolds

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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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Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, IN, USA

    Fabrice Baudoin & Jing Wang

Authors
  1. Fabrice Baudoin
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  2. Jing Wang
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Correspondence to Fabrice Baudoin.

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First author was supported in part by NSF Grant DMS 0907326.

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Baudoin, F., Wang, J. Curvature Dimension Inequalities and Subelliptic Heat Kernel Gradient Bounds on Contact Manifolds. Potential Anal 40, 163–193 (2014). https://doi.org/10.1007/s11118-013-9345-x

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  • DOI: https://doi.org/10.1007/s11118-013-9345-x

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