Heat and entropy flows in Carnot groups

Luigi Ambrosio ^[1] ; Giorgio Stefani ^[1]
1. [1] Scuola Normale Superiore, Pisa
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 1, 2020, págs. 257-290
Idioma: inglés
DOI: 10.4171/rmi/1129
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Resumen
- 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.