# Heat and entropy flows in Carnot groups

created by stefani on 04 Jan 2018
modified on 08 Jan 2018

[BibTeX]

Submitted Paper

Inserted: 4 jan 2018
Last Updated: 8 jan 2018

Year: 2018

ArXiv: 1801.01300 PDF

Abstract:

In this paper, we extend the result obtained in Juillet, Calc. Var. Partial Differential Equations (2014) for the Heisenberg group to any Carnot group $\mathbb{G}$. Namely, we prove the correspondence between solutions of the sub-elliptic heat equation in $\mathbb{G}$ and gradient flows of the relative entropy functional in the Wasserstein space of probability measures on $\mathbb{G}$.