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 SU(2) group.
Generalized Bakry–Émery Curvature Condition and Equivalent Entropic Inequalities in Groups
Stefani G.
2022
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 SU(2) group.
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Stefani - Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups.pdf
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