{
  "id": "1704.05131",
  "version": "v1",
  "published": "2017-04-17T21:30:30.000Z",
  "updated": "2017-04-17T21:30:30.000Z",
  "title": "A free boundary problem on three-dimensional cones",
  "authors": [
    "Mark Allen"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a free boundary problem on cones depending on a parameter c and study when the free boundary is allowed to pass through the vertex of the cone. We show that when the cone is three-dimensional and c is large enough, the free boundary avoids the vertex. We also show that when c is small enough but still positive, the free boundary is allowed to pass through the vertex. This establishes 3 as the critical dimension for which the free boundary may pass through the vertex of a right circular cone. In view of the well-known connection between area-minimizing surfaces and the free boundary problem under consideration, our result is analogous to a result of Morgan that classifies when an area-minimizing surface on a cone passes through the vertex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-17T21:30:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R35",
      "35R01",
      "35J20",
      "49N60"
    ],
    "keywords": [
      "free boundary problem",
      "three-dimensional cones",
      "free boundary avoids",
      "right circular cone",
      "area-minimizing surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}