{
  "id": "1712.08454",
  "version": "v1",
  "published": "2017-12-22T14:10:41.000Z",
  "updated": "2017-12-22T14:10:41.000Z",
  "title": "Uniqueness of critical points of solutions to the mean curvature equation with Neumann and Robin boundary conditions",
  "authors": [
    "Haiyun Deng",
    "Hairong Liu",
    "Long Tian"
  ],
  "comment": "11pages, 4figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we investigate the critical points of solutions to the prescribed constant mean curvature equation with Neumann and Robin boundary conditions respectively in a smooth, bounded and strictly convex domain $\\Omega$ of $\\mathbb{R}^{n}(n\\geq2)$. Firstly, we show the nondegeneracy and uniqueness of the critical points of solutions in a planar domain by using the local Chen \\& Huang's comparison technique and the geometric properties of approximate curved surfaces at the nondegenerate critical points. Secondly, we deduce the uniqueness and nondegeneracy of the critical points of solutions in a rotationally symmetric domain of $\\mathbb{R}^{n}(n\\geq3)$ by the projection of higher dimension space onto two dimension plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-22T14:10:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J93",
      "35J25",
      "35B38"
    ],
    "keywords": [
      "critical points",
      "robin boundary conditions",
      "uniqueness",
      "prescribed constant mean curvature equation",
      "huangs comparison technique"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}