{
  "id": "0809.2172",
  "version": "v2",
  "published": "2008-09-12T10:41:49.000Z",
  "updated": "2009-02-19T15:54:59.000Z",
  "title": "Concentration-compactness phenomena in the higher order Liouville's equation",
  "authors": [
    "Luca Martinazzi"
  ],
  "comment": "26 pages, revised version",
  "journal": "J. Funct. Anal. 256 (2009), 3743-3771",
  "doi": "10.1016/j.jfa.2009.02.017",
  "categories": [
    "math.AP",
    "math.DG",
    "math.FA"
  ],
  "abstract": "We investigate different concentration-compactness phenomena related to the Q-curvature in arbitrary even dimension. We first treat the case of an open domain in $R^{2m}$, then that of a closed manifold and, finally, the particular case of the sphere $S^{2m}$. In all cases we allow the sign of the Q-curvature to vary, and show that in the case of a closed manifold, contrary to the case of open domains in $R^{2m}$, concentration phenomena can occur only at points of positive Q-curvature. As a consequence, on a locally conformally flat manifold of non-positive Euler characteristic we always have compactness.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-02-19T15:54:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higher order liouvilles equation",
      "concentration-compactness phenomena",
      "open domain",
      "closed manifold",
      "q-curvature"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.2172M"
    }
  }
}