{
  "id": "math/0104041",
  "version": "v1",
  "published": "2001-04-03T15:43:36.000Z",
  "updated": "2001-04-03T15:43:36.000Z",
  "title": "Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries",
  "authors": [
    "Veronica Felli",
    "Mohameden Ould Ahmedou"
  ],
  "comment": "34 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is devoted to the study of a problem arising from a geometric context, namely the conformal deformation of a Riemannian metric to a scalar flat one having constant mean curvature on the boundary. By means of blow-up analysis techniques and the Positive Mass Theorem, we show that on locally conformally flat manifolds with umbilic boundary all metrics stay in a compact set with respect to the $C^2$-norm and the total Leray-Schauder degree of all solutions is equal to -1. Then we deduce from this compactness result the existence of at least one solution to our problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-04-03T15:43:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "53C21",
      "58G30"
    ],
    "keywords": [
      "compactness result",
      "conformal deformation",
      "riemannian metric",
      "constant mean curvature",
      "total leray-schauder degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......4041F"
    }
  }
}