{
  "id": "0806.1645",
  "version": "v1",
  "published": "2008-06-10T12:37:53.000Z",
  "updated": "2008-06-10T12:37:53.000Z",
  "title": "Hölder Regularity of Two-Dimensional Almost-Minimal Sets in $\\R^n$",
  "authors": [
    "Guy David"
  ],
  "comment": "150 pages. Submitted in May 2007",
  "categories": [
    "math.CA"
  ],
  "abstract": "We give a different and probably more elementary proof of a good part of Jean Taylor's regularity theorem for Almgren almost-minimal sets of dimension 2 in $\\R^3$. We use this opportunity to settle some details about almost-minimal sets, extend a part of Taylor's result to almost-minimal sets of dimension 2 in $\\R^n$, and give the expected characterization of the closed sets $E$ of dimension 2 in $\\R^3$ that are minimal, in the sense that $H^2(E\\setminus F) \\leq H^2(F\\setminus E)$ for every closed set $F$ such that there is a bounded set $B$ so that $F=E$ out of $B$ and $F$ separates points of $\\R^3 \\setminus B$ that $E$ separates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-10T12:37:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49K99",
      "49Q20"
    ],
    "keywords": [
      "two-dimensional almost-minimal sets",
      "hölder regularity",
      "jean taylors regularity theorem",
      "almgren almost-minimal sets",
      "closed set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 150,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.1645D"
    }
  }
}