{
  "id": "1410.7463",
  "version": "v1",
  "published": "2014-10-28T00:32:32.000Z",
  "updated": "2014-10-28T00:32:32.000Z",
  "title": "Some remarks on stability of cones for the one-phase free boundary problem",
  "authors": [
    "David Jerison",
    "Ovidiu Savin"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that stable cones for the one-phase free boundary problem are hyperplanes in dimension $4$. As a corollary, both one and two-phase energy minimizing hypersurfaces are smooth in dimension $4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-28T00:32:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "one-phase free boundary problem",
      "two-phase energy minimizing hypersurfaces",
      "hyperplanes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.7463J"
    }
  }
}