{
  "id": "1305.2669",
  "version": "v1",
  "published": "2013-05-13T03:54:50.000Z",
  "updated": "2013-05-13T03:54:50.000Z",
  "title": "Curvature estimates for the level sets of solutions of the Monge-Ampère equation $\\det D^2 u=1$",
  "authors": [
    "Chuanqiang Chen",
    "Xinan Ma",
    "Shujun Shi"
  ],
  "comment": "This paper is part of the PhD thesis of the Third author Shujun Shi, and is submitted in Jan. 2013",
  "categories": [
    "math.AP"
  ],
  "abstract": "For the Monge-Amp\\`{e}re equation $\\det D^2 u=1$, we find new auxiliary curvature functions which attain respective maximum on the boundary. Moreover, we obtain the upper bounded estimates for the Gauss curvature and mean curvature of the level sets for the solution to this equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-13T03:54:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J65"
    ],
    "keywords": [
      "level sets",
      "curvature estimates",
      "monge-ampère equation",
      "auxiliary curvature functions",
      "attain respective maximum"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.2669C"
    }
  }
}