Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups

Abstract

We study a generalization of the Bakry-Émery pointwise gradient estimate for the heat semigroup and its equivalence with some entropic inequalities along the heat flow and Wasserstein geodesics for metric-measure spaces with a suitable group structure. Our main result applies to Carnot groups of any step and to the $\mathbb{SU}(2)$ group.

76 pages

References in corpus (3)

• On gradient bounds for the heat kernel on the Heisenberg group
• Curvature-dimension estimates for the Laplace-Beltrami operator of a totally geodesic foliation
• Branching geodesics in sub-Riemannian geometry

Cited by in corpus (1)

• Sub-Riemannian geometry on some step-two Carnot groups