Published Paper
Inserted: 4 jan 2018
Last Updated: 3 oct 2021
Journal: Rev. Mat. Iberoam.
Number: 1
Pages: 257--290
Year: 2020
Doi: 10.4171/rmi/1129
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.
Keywords: entropy, Gradient Flow, Carnot group, sub-elliptic heat equation
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