{
  "id": "1408.5233",
  "version": "v1",
  "published": "2014-08-22T09:13:52.000Z",
  "updated": "2014-08-22T09:13:52.000Z",
  "title": "One-sided curvature estimates for H-disks",
  "authors": [
    "William H. Meeks III",
    "Giuseppe Tinaglia"
  ],
  "comment": "13 pages, 1 figure",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper we prove an extrinsic one-sided curvature estimate for disks embedded in $\\mathbb{R}^3$ with constant mean curvature which is independent of the value of the constant mean curvature. We apply this extrinsic one-sided curvature estimate in [24] to prove to prove a weak chord arc type result for these disks. In Section 4 we apply this weak chord arc result to obtain an intrinsic version of the one-sided curvature estimate for disks embedded in $\\mathbb{R}^3$ with constant mean curvature. In a natural sense, these one-sided curvature estimates generalize respectively, the extrinsic and intrinsic one-sided curvature estimates for minimal disks embedded in $\\mathbb{R}^3$ given by Colding and Minicozzi in Theorem 0.2 of [9] and in Corollary 0.8 of [10].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-22T09:13:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10"
    ],
    "keywords": [
      "constant mean curvature",
      "extrinsic one-sided curvature estimate",
      "weak chord arc type result",
      "curvature estimates generalize"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.5233M"
    }
  }
}