Bakry-Émery curvature and model spaces in sub-Riemannian geometry

Abstract : We prove comparison theorems for the sub-Riemannian distortion coefficients appearing in interpolation inequalities. These results, which are equivalent to a sub-Laplacian comparison theorem for the sub-Riemannian distance, are obtained by introducing a suitable notion of sub-Riemannian Bakry-Émery curvature. The model spaces for comparison are variational problems coming from optimal control theory. As an application we establish the sharp measure contraction property for 3-Sasakian manifolds satisfying a suitable curvature bound.
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Contributor : Luca Rizzi <>
Submitted on : Monday, June 24, 2019 - 9:39:54 AM
Last modification on : Wednesday, October 16, 2019 - 1:23:54 AM

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  • HAL Id : hal-02163180, version 1
  • ARXIV : 1906.08307


Davide Barilari, Luca Rizzi. Bakry-Émery curvature and model spaces in sub-Riemannian geometry. 2019. ⟨hal-02163180⟩



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