{
  "id": "1303.4281",
  "version": "v1",
  "published": "2013-03-18T15:13:54.000Z",
  "updated": "2013-03-18T15:13:54.000Z",
  "title": "On representation of boundary integrals involving the mean curvature for mean-convex domains",
  "authors": [
    "Yoshikazu Giga",
    "Giovanni Pisante"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Given a mean-convex domain $\\Omega\\subset \\R^n$ with boundary of class $C^{2,1}$, we provide a representation formula for a boundary integral of the type \\[ \\int_{\\partial \\Omega} f(k(x)) \\, d\\mathcal{H}^{n-1} \\] where $k\\geq 0$ is the mean curvature of $\\partial \\Omega$ and $f$ is non-increasing and sufficiently regular, in terms of volume integrals and defect measure on the ridge set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-18T15:13:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean curvature",
      "mean-convex domain",
      "boundary integral",
      "representation formula",
      "volume integrals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.4281G"
    }
  }
}