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Generalized Bakry–Émery Curvature Condition and Equivalent Entropic Inequalities in Groups

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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 \({\mathbb {S}}{\mathbb {U}}(2)\) group.

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Acknowledgements

The author thanks Luigi Ambrosio and Giuseppe Savaré for helpful discussions and many valuable suggestions about the subject. The author also thanks the anonymous referee for precious comments and for pointing the reference [145]. The author is partially supported by the ERC Starting Grant 676675 FLIRT – Fluid Flows and Irregular Transport. The author is a member of INdAM and is partially supported by the INdAM–GNAMPA Project 2020 Problemi isoperimetrici con anisotropie (n. prot. U-UFMBAZ-2020-000798 15-04-2020)

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    Giorgio Stefani

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Stefani, G. Generalized Bakry–Émery Curvature Condition and Equivalent Entropic Inequalities in Groups. J Geom Anal 32, 136 (2022). https://doi.org/10.1007/s12220-021-00762-6

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