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

Luca Tamanini
CEREMADE, Université Paris-Dauphine
https://scholar.google.com/citations?user=RhMC_jYAAAAJ&hl=it

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.

https://arxiv.org/abs/1907.07163

http://cvgmt.sns.it/person/2247/

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