{
  "id": "math/0106219",
  "version": "v4",
  "published": "2001-06-26T13:34:25.000Z",
  "updated": "2002-05-22T07:01:38.000Z",
  "title": "On a geometric equation with critical nonlinearity on the boundary",
  "authors": [
    "Veronica Felli",
    "Mohameden Ould Ahmedou"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "A theorem of Escobar asserts that, on a positive three dimensional smooth compact Riemannian manifold with boundary which is not conformally equivalent to the standard three dimensional ball, a necessary and sufficient condition for a $C^2$ function $H$ to be the mean curvature of some conformal flat metric is that $H$ is positive somewhere. We show that, when the boundary is umbilic and the function $H$ is positive everywhere, all such metrics stay in a compact set with respect to the $C^2$ norm and the total degree of all solutions is equal to -1.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2002-05-22T07:01:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "53C21",
      "58G30"
    ],
    "keywords": [
      "geometric equation",
      "critical nonlinearity",
      "dimensional smooth compact riemannian manifold",
      "conformal flat metric",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......6219F"
    }
  }
}