Calculus of Variations and Geometric Measure Theory

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 07 Jun 2020


Published Paper

Inserted: 19 jun 2019
Last Updated: 7 jun 2020

Journal: Mathematische Annalen
Volume: 377
Pages: 435–482
Year: 2020
Doi: 10.1007/s00208-020-01982-x

ArXiv: 1906.08307 PDF


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.