CEREMADE, Université Paris-Dauphine
Date(s) : 22/03/2019 iCal
11 h 00 min - 12 h 00 min
Aim of this talk is to show that a dimension-free Harnack inequality on an infinitesimally Hilbertian metric measure space where the heat semigroup admits an integral representation in terms of a kernel is suffcient to deduce a sharp upper Gaussian estimate for such kernel. As intermediate step, we prove the local logarithmic Sobolev inequality (known to be equivalent to a lower bound on the Ricci curvature tensor in smooth Riemannian manifolds). Both results are new also in the more regular framework of RCD(K,∞) spaces.