Generalized Bakry–Émery Curvature Condition and Equivalent Entropic Inequalities in Groups
Copyright policy )Generalized Bakry–Émery Curvature Condition and Equivalent Entropic Inequalities in Groups
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
- University of Padua Italy
- University of Basel Switzerland
Bakry-Émery curvature condition, metric-measure space, Carnot group, entropic inequalities, Bakry–Émery curvature condition; Carnot group; Entropic inequalities; Entropy; Gamma calculus; Metric-measure space; SU(2) group; Topological groups; Wasserstein distance, Metric Geometry (math.MG), 47D07, 28D20 (Primary) 53C17 (Secondary), \(\mathbb{SU}(2)\) group, Sub-Riemannian geometry, gamma calculus, Mathematics - Metric Geometry, FOS: Mathematics, Wasserstein distance, Entropy and other invariants, entropy, Markov semigroups and applications to diffusion processes, topological groups
Bakry-Émery curvature condition, metric-measure space, Carnot group, entropic inequalities, Bakry–Émery curvature condition; Carnot group; Entropic inequalities; Entropy; Gamma calculus; Metric-measure space; SU(2) group; Topological groups; Wasserstein distance, Metric Geometry (math.MG), 47D07, 28D20 (Primary) 53C17 (Secondary), \(\mathbb{SU}(2)\) group, Sub-Riemannian geometry, gamma calculus, Mathematics - Metric Geometry, FOS: Mathematics, Wasserstein distance, Entropy and other invariants, entropy, Markov semigroups and applications to diffusion processes, topological groups
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