From Harnack inequality to heat kernel estimates on metric measure spaces and applications

Luca Tamanini
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.


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