{
  "id": "2206.06006",
  "version": "v1",
  "published": "2022-06-13T09:50:48.000Z",
  "updated": "2022-06-13T09:50:48.000Z",
  "title": "Prescribing $Q$-curvature on even-dimensional manifolds with conical singularities",
  "authors": [
    "Aleks Jevnikar",
    "Yannick Sire",
    "Wen Yang"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "On a $2m$-dimensional closed manifold we investigate the existence of prescribed $Q$-curvature metrics with conical singularities. We present here a general existence and multiplicity result in the supercritical regime. To this end, we first carry out a blow-up analysis of a $2m$th-order PDE associated to the problem and then apply a variational argument of min-max type. For $m>1$, this seems to be the first existence result for supercritical conic manifolds different from the sphere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-13T09:50:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conical singularities",
      "even-dimensional manifolds",
      "first existence result",
      "first carry",
      "prescribing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}