Bakry-\'Emery curvature and model spaces in sub-Riemannian geometry
Differential Geometry
2020-03-18 v2 Analysis of PDEs
Optimization and Control
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-\'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.
Keywords
Cite
@article{arxiv.1906.08307,
title = {Bakry-\'Emery curvature and model spaces in sub-Riemannian geometry},
author = {Davide Barilari and Luca Rizzi},
journal= {arXiv preprint arXiv:1906.08307},
year = {2020}
}
Comments
37 pages; v2: added section 6.2 on the weighted Heisenberg group, fixed typos. Final version to appear on Mathematische Annalen