Preprint

Inserted: 16 jul 2019
Last Updated: 16 jul 2019

Year: 2019

Abstract:

Aim of this short note 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 sufficient 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 $RCD(K,\infty)$ spaces.

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• heatkernel.pdf