{
  "id": "2210.15774",
  "version": "v1",
  "published": "2022-10-27T21:14:20.000Z",
  "updated": "2022-10-27T21:14:20.000Z",
  "title": "Sharp log-Sobolev inequalities in ${\\sf CD}(0,N)$ spaces with applications",
  "authors": [
    "Zoltán M. Balogh",
    "Alexandru Kristály",
    "Francesca Tripaldi"
  ],
  "comment": "33 pages",
  "categories": [
    "math.AP",
    "math.DG",
    "math.FA"
  ],
  "abstract": "Given $p,N>1,$ we prove the sharp $L^p$-log-Sobolev inequality on metric measure spaces satisfying the ${\\sf CD}(0,N)$ condition, where the optimal constant involves the asymptotic volume ratio of the space. Combining the sharp $L^p$-log-Sobolev inequality with the Hamilton-Jacobi inequality, we establish a sharp hypercontractivity estimate for the Hopf-Lax semigroup in ${\\sf CD}(0,N)$ spaces. Moreover, a Gaussian-type $L^2$-log-Sobolev inequality is also obtained in ${\\sf RCD}(0,N)$ spaces. Our results are new, even in the smooth setting of Riemannian/Finsler manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-27T21:14:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "log-sobolev inequality",
      "sharp log-sobolev inequalities",
      "applications",
      "asymptotic volume ratio",
      "sharp hypercontractivity estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}