Calculus of Variations and Geometric Measure Theory

G. Stefani

Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups

created by stefani on 29 Aug 2020
modified on 20 Oct 2021


Accepted Paper

Inserted: 29 aug 2020
Last Updated: 20 oct 2021

Journal: J. Geom. Anal.
Year: 2020

ArXiv: 2008.13731 PDF


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.