{
  "id": "1310.8101",
  "version": "v1",
  "published": "2013-10-30T10:57:23.000Z",
  "updated": "2013-10-30T10:57:23.000Z",
  "title": "The weak Cartan property for the p-fine topology on metric spaces",
  "authors": [
    "Anders Björn",
    "Jana Björn",
    "Visa Latvala"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the p-fine topology on complete metric spaces equipped with a doubling measure supporting a p-Poincare inequality, 1 < p< oo. We establish a weak Cartan property, which yields characterizations of the p-thinness and the p-fine continuity, and allows us to show that the p-fine topology is the coarsest topology making all p-superharmonic functions continuous. Our p-harmonic and superharmonic functions are defined by means of scalar-valued upper gradients and do not rely on a vector-valued differentiable structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-30T10:57:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31E05",
      "30L99",
      "31C40",
      "31C45",
      "35J92",
      "49Q20"
    ],
    "keywords": [
      "weak cartan property",
      "p-fine topology",
      "coarsest topology",
      "complete metric spaces",
      "yields characterizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.8101B"
    }
  }
}