{
  "id": "1804.09261",
  "version": "v1",
  "published": "2018-04-24T21:20:30.000Z",
  "updated": "2018-04-24T21:20:30.000Z",
  "title": "Gluing metrics with prescribed $Q$-curvature and different asymptotic behaviour in dimension $6$",
  "authors": [
    "Ali Hyder",
    "Luca Martinazzi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We show a new example of blow-up behaviour for the prescribed $Q$-curvature equation in dimension $6$, namely given a sequence $(V_k)\\subset C^0(\\mathbb{R}^6)$ suitably converging we construct a sequence $(u_k)$ of radially symmetric solutions to the equation $$(-\\Delta)^3 u_k=V_k e^{6 u_k} \\quad \\text{in }\\mathbb{R}^6,$$ with $u_k$ blowing up at the origin and on a sphere. We also prove sharp blow-up estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-24T21:20:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic behaviour",
      "gluing metrics",
      "sharp blow-up estimates",
      "blow-up behaviour",
      "curvature equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}