Calculus of Variations and Geometric Measure Theory
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D. Barilari - L. Rizzi

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

created by barilari on 19 Jun 2019
modified by rizzi1 on 26 Mar 2020

[BibTeX]

Accepted Paper

Inserted: 19 jun 2019
Last Updated: 26 mar 2020

Journal: Mathematische Annalen
Year: 2020
Doi: 10.1007/s00208-020-01982-x

ArXiv: 1906.08307 PDF

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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