Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups. (English) Zbl 07493867
Summary: 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.
MSC:
| 47D07 | Markov semigroups and applications to diffusion processes |
| 28D20 | Entropy and other invariants |
| 53C17 | Sub-Riemannian geometry |
Keywords:
Bakry-Émery curvature condition; metric-measure space; Carnot group; \(\mathbb{SU}(2)\) group; topological groups; gamma calculus; entropy; entropic inequalities; Wasserstein distanceReferences:
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