{
  "id": "math/0306141",
  "version": "v1",
  "published": "2003-06-08T21:16:17.000Z",
  "updated": "2003-06-08T21:16:17.000Z",
  "title": "Some Properties of the Distance Function and a Conjecture of De Giorgi",
  "authors": [
    "Manolo Eminenti",
    "Carlo Mantegazza"
  ],
  "journal": "J. Geom. Anal. 14 (2004), no. 2, 267-279",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We analyse the geometric properties of the high derivatives of the distance function from a submanifold of the Euclidean space. In particular, we show some relations with the second fundamental form and its covariant derivatives of independent interest. As an application we prove a conjecture of Ennio De Giorgi on the evolution of submanifolds of the Euclidean space by the gradient of functionals depending on the derivatives of the distance function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-06-08T21:16:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A07",
      "53A55"
    ],
    "keywords": [
      "distance function",
      "conjecture",
      "euclidean space",
      "second fundamental form",
      "geometric properties"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......6141E"
    }
  }
}