Potential Analysis

, Volume 40, Issue 2, pp 163–193

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



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.


Curvature dimension inequality Γ2 calculus Contact manifold Bochner’s formula Gradient bounds for the heat semigroup 

Mathematics Subject Classifications (2010)

53C17 53C25 58J35 


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA

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