{
  "id": "1110.4615",
  "version": "v2",
  "published": "2011-10-20T19:22:35.000Z",
  "updated": "2012-01-31T23:31:09.000Z",
  "title": "The Yamabe problem for Q-curvature",
  "authors": [
    "David Raske"
  ],
  "comment": "This paper has been withdrawn by the author because \"On the $k$th order Yamabe problem\" has made it obsolete",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper we demonstrate that under general conditions there exists a metric in the conformal class of an arbitrary metric on a smooth, closed Riemannian manifold of dimension greater than four such that the $Q$-curvature of the metric is a constant. Existence of solutions is obtained through the combination of variational methods, second order Sobolev inequalities, and the $W^{2,2}$ blow-up theory developed by Hebey and Robert. Positivity of the solutions is obtained from a novel argument proven here for the first time that is rooted in the conformal covariance property of the Paneitz-Branson operator and the positive semidefiniteness of the second derivative of a $C^2$ function at a local minimum.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-31T23:31:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E11",
      "58J05",
      "53C21",
      "53C25"
    ],
    "keywords": [
      "yamabe problem",
      "q-curvature",
      "second order sobolev inequalities",
      "novel argument proven",
      "conformal covariance property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.4615R"
    }
  }
}