{
  "id": "1401.6480",
  "version": "v3",
  "published": "2014-01-25T00:46:28.000Z",
  "updated": "2015-04-12T08:36:56.000Z",
  "title": "A new proof of Savin's theorem on Allen-Cahn equations",
  "authors": [
    "Kelei Wang"
  ],
  "comment": "59 pages. Comments are welcome",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we establish an improvement of tilt-excess decay estimate for the Allen-Cahn equation, and use this to give a new proof of Savin's theorem on the uniform $C^{1,\\alpha}$ regularity of flat level sets, which then implies the one dimensional symmetry of minimizers in $\\mathbb{R}^n$ for $n\\leq 7$. This generalizes Allard's $\\varepsilon$-regularity theorem for stationary varifolds to the setting of Allen-Cahn equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-25T00:46:28.000Z",
      "comment": "56 pages. Comments are welcome",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-26T05:22:01.000Z",
      "comment": "57 pages. Comments are welcome",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-04-12T08:36:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B06",
      "35B06",
      "35B08",
      "35B25",
      "35J91"
    ],
    "keywords": [
      "allen-cahn equation",
      "savins theorem",
      "tilt-excess decay estimate",
      "flat level sets",
      "stationary varifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.6480W"
    }
  }
}