{
  "id": "1405.0186",
  "version": "v2",
  "published": "2014-05-01T15:21:24.000Z",
  "updated": "2015-07-18T10:20:52.000Z",
  "title": "Characterizations of sets of finite perimeter using heat kernels in metric spaces",
  "authors": [
    "Niko Marola",
    "Michele Miranda Jr.",
    "Nageswari Shanmugalingam"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The overarching goal of this paper is to link the notion of sets of finite perimeter (a concept associated with $N^{1,1}$-spaces) and the theory of heat semigroups (a concept related to $N^{1,2}$-spaces) in the setting of metric measure spaces whose measure is doubling and supports a $1$-Poincar\\'e inequality. We prove a characterization of sets of finite perimeter in terms of a short time behavior of the heat semigroup in such metric spaces. We also give a new characterization of ${\\rm BV}$ functions in terms of a near-diagonal energy in this general setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-01T15:21:24.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-07-18T10:20:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite perimeter",
      "metric spaces",
      "heat kernels",
      "characterization",
      "heat semigroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.0186M"
    }
  }
}