{
  "id": "math/0410140",
  "version": "v2",
  "published": "2004-10-06T06:31:52.000Z",
  "updated": "2005-01-20T07:21:02.000Z",
  "title": "Compactness of solutions to some geometric fourth-order equations",
  "authors": [
    "Andrea Malchiodi"
  ],
  "comment": "32 pages, fixed some bug in the previous version",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant $Q$-curvature. As a byproduct of our method, we also obtain compactness of such metrics.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-01-20T07:21:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B33",
      "35J35",
      "53A30",
      "53C21"
    ],
    "keywords": [
      "geometric fourth-order equations",
      "compactness",
      "fourth order equations",
      "exponential nonlinearities",
      "main estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10140M"
    }
  }
}