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.

arXiv comment76 pages

References in corpus (22)

• Metric measure spaces with Riemannian Ricci curvature bounded from below
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
• Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
• Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure
• Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in RCD(K,\infty) metric measure spaces
• On gradient bounds for the heat kernel on the Heisenberg group
• Eulerian calculus for the displacement convexity in the Wasserstein distance
• Sub-Riemannian curvature in contact geometry
• Sharp measure contraction property for generalized H-type Carnot groups
• Optimal maps in essentially non-branching spaces
• On Jacobi fields and canonical connection in sub-Riemannian geometry
• Sub-Riemannian interpolation inequalities
• Comparison theorems for conjugate points in sub-Riemannian geometry
• Measure contraction properties of Carnot groups
• Dimensional contraction via Markov transportation distance
• Infinitesimal Hilbertianity of weighted Riemannian manifolds
• Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds
• Measure rigidity of Ricci curvature lower bounds
• Curvature-dimension estimates for the Laplace-Beltrami operator of a totally geodesic foliation
• Branching geodesics in sub-Riemannian geometry
• Bakry-Émery curvature and model spaces in sub-Riemannian geometry

Cited by in corpus (1)

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