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arXiv · 1906.08307

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

Davide Barilari·Luca Rizzi
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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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Davide Barilari, Luca Rizzi. 2020-03-17. Bakry-Émery curvature and model spaces in sub-Riemannian geometry. https://doi.org/10.1007/s00208-020-01982-x

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