{
  "id": "1808.09687",
  "version": "v1",
  "published": "2018-08-29T08:56:19.000Z",
  "updated": "2018-08-29T08:56:19.000Z",
  "title": "Minimality for unions of 2-dimensional minimal cones with non-isolated singularities",
  "authors": [
    "Xiangyu Liang"
  ],
  "comment": "78 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this article we prove that for a large class of 2-dimensional minimal cones (including almost all 2-dimensional minimal cones that we know), the almost orthogonal union of any two of them is still a minimal cone. Comparing to existing results for minimality of almost orthogonal union of planes \\cite{2p,2ptopo}, here we are dealing with unions of cones with non isolated singularities, which results in a series of essential difficulties, and new ideas are required. The proof in this article can be generalized to other types of minimalities, e.g. topological minimality, Reifenberg minimality, etc..",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-29T08:56:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A75",
      "49Q20",
      "49K21",
      "49K99"
    ],
    "keywords": [
      "minimal cone",
      "non-isolated singularities",
      "orthogonal union",
      "reifenberg minimality",
      "essential difficulties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 78,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}