Revista Matemática Iberoamericana
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Published online: 2019-10-21
Heat and entropy flows in Carnot groupsLuigi Ambrosio and Giorgio Stefani (1) Scuola Normale Superiore, Pisa, Italy
(2) Scuola Normale Superiore, Pisa, Italy
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: Carnot group, entropy, gradient flow, sub-elliptic heat equation
Ambrosio Luigi, Stefani Giorgio: Heat and entropy flows in Carnot groups. Rev. Mat. Iberoam. 36 (2020), 257-290. doi: 10.4171/rmi/1129