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Article Dans Une Revue Mathematische Annalen Année : 2020

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

Résumé

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.

Dates et versions

hal-02163180 , version 1 (24-06-2019)

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Citer

Davide Barilari, Luca Rizzi. Bakry-Émery curvature and model spaces in sub-Riemannian geometry. Mathematische Annalen, 2020, 377 (1-2), pp.435-482. ⟨10.1007/s00208-020-01982-x⟩. ⟨hal-02163180⟩
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