{
  "id": "1207.5129",
  "version": "v2",
  "published": "2012-07-21T12:10:20.000Z",
  "updated": "2014-06-21T10:03:53.000Z",
  "title": "$C^{1,α}$-regularity for surfaces with $H$ in $L^p$",
  "authors": [
    "Theodora Bourni",
    "Giuseppe Tinaglia"
  ],
  "comment": "We wish to express our gratitude to the referee for valuable suggestions. In particular the proof of Corollary 3.2 is now simpler",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper we prove several results on the geometry of surfaces immersed in $\\mathbf R^3$ with small or bounded $L^2$ norm of $|A|$. For instance, we prove that if the $L^2$ norm of $|A|$ and the $L^p$ norm of $H$, $p>2$, are sufficiently small, then such a surface is graphical away from its boundary. We also prove that given an embedded disk with bounded $L^2$ norm of $|A|$, not necessarily small, then such a disk is graphical away from its boundary, provided that the $L^p$ norm of $H$ is sufficiently small, $p>2$. These results are related to previous work of Schoen-Simon and Colding-Minicozzi.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-21T10:03:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "regularity",
      "graphical away",
      "sufficiently small",
      "embedded disk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.5129B"
    }
  }
}