{
  "id": "1810.11577",
  "version": "v1",
  "published": "2018-10-27T02:23:38.000Z",
  "updated": "2018-10-27T02:23:38.000Z",
  "title": "Faber-Krahn type inequalities and uniqueness of positive solutions on metric measure spaces",
  "authors": [
    "Anup Biswas",
    "Janna Lierl"
  ],
  "categories": [
    "math.PR",
    "math.AP",
    "math.SP"
  ],
  "abstract": "We consider a general class of metric measure spaces equipped with a regular Dirichlet form and then provide a lower bound on the hitting time probabilities of the associated Hunt process. Using these estimates we establish (i) a generalization of the classical Lieb's inequality on metric measure spaces and (ii) uniqueness of nonnegative super-solutions on metric measure spaces. Finally, using heat-kernel estimates we generalize the local Faber-Krahn inequality recently obtained in [LS18].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-27T02:23:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric measure spaces",
      "faber-krahn type inequalities",
      "positive solutions",
      "uniqueness",
      "local faber-krahn inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}