Resumen de Heat and entropy flows in Carnot groups

Luigi Ambrosio, Giorgio Stefani

• We prove the correspondence between the solutions of the sub-elliptic heat equation in a Carnot group G and the gradient flows of the relative entropy functional in the Wasserstein space of probability measures on 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, the n-dimensional Heisenberg group.