JournalsrmiVol. 36, No. 1pp. 257–290

Heat and entropy flows in Carnot groups

  • Luigi Ambrosio

    Scuola Normale Superiore, Pisa, Italy
  • Giorgio Stefani

    Scuola Normale Superiore, Pisa, Italy
Heat and entropy flows in Carnot groups cover

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Abstract

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

Cite this article

Luigi Ambrosio, Giorgio Stefani, Heat and entropy flows in Carnot groups. Rev. Mat. Iberoam. 36 (2020), no. 1, pp. 257–290

DOI 10.4171/RMI/1129