{
  "id": "0709.1776",
  "version": "v2",
  "published": "2007-09-12T09:06:52.000Z",
  "updated": "2008-07-24T01:35:53.000Z",
  "title": "Regularity of C^{1} smooth surfaces with prescribed p-mean curvature in the Heisenberg group",
  "authors": [
    "Jih-Hsin Cheng",
    "Jenn-Fang Hwang",
    "Paul Yang"
  ],
  "comment": "30 pages",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We consider a $C^{1}$ smooth surface with prescribed $p$(or $H$)-mean curvature in the 3-dimensional Heisenberg group. Assuming only the prescribed $p$-mean curvature $H\\in C^{0},$ we show that any characteristic curve is $C^{2}$ smooth and its (line) curvature equals $-H$ in the nonsingular domain$.$ By introducing characteristic coordinates and invoking the jump formulas along characteristic curves, we can prove that the Legendrian (or horizontal) normal gains one more derivative. Therefore the seed curves are $C^{2}$ smooth. We also obtain the uniqueness of characteristic and seed curves passing through a common point under some mild conditions, respectively. These results can be applied to more general situations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-07-24T01:35:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L80",
      "35J70",
      "32V20",
      "53A10",
      "49Q10"
    ],
    "keywords": [
      "prescribed p-mean curvature",
      "heisenberg group",
      "smooth surface",
      "regularity",
      "characteristic curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.1776C"
    }
  }
}