{
  "id": "1907.07163",
  "version": "v1",
  "published": "2019-07-16T17:45:38.000Z",
  "updated": "2019-07-16T17:45:38.000Z",
  "title": "From Harnack inequality to heat kernel estimates on metric measure spaces and applications",
  "authors": [
    "Luca Tamanini"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "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 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 $RCD(K,\\infty)$ spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-16T17:45:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heat kernel estimates",
      "harnack inequality",
      "applications",
      "infinitesimally hilbertian metric measure space",
      "sharp upper gaussian estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}