Heat and entropy flows in Carnot groups

Abstract

We prove the correspondence between the solutions of the sub-elliptic heat equation in a Carnot group $\mathbb{G}$ and the gradient flows of the relative entropy functional in the Wasserstein space of probability measures on $\mathbb{G}$. Our result completely answers a question left open in a previous paper by N. Juillet, where the same correspondence was proved for $\mathbb{G}={\mathbb{H}}^n$, the $n$-dimensional Heisenberg group.

28 pages

References in corpus (1)

• Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure