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Bakry-\'Emery curvature and model spaces in sub-Riemannian geometry

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arxiv 1906.08307 v2 pith:AWXCQWZK submitted 2019-06-19 math.DG math.APmath.OC

Davide Barilari , Luca Rizzi This is my paper · ORCID
classification math.DGmath.APmath.OC
keywords sub-riemanniancomparisoncurvaturebakry-emerymodelspacessuitable
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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-\'Emery 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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  1. The Quasi Curvature-Dimension Condition with applications to sub-Riemannian manifolds

    math.FA 2019-08 accept novelty 8.0 of 10

    A quasi-convex relaxation of the curvature-dimension condition gives dimension-independent Poincaré and log-Sobolev constants on Heisenberg groups and other sub-Riemannian manifolds, up to a universal factor.

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