{
  "id": "2308.12656",
  "version": "v1",
  "published": "2023-08-24T08:56:57.000Z",
  "updated": "2023-08-24T08:56:57.000Z",
  "title": "Asymptotic behavior of conformal metrics with null Q-curvature",
  "authors": [
    "Mingxiang Li"
  ],
  "comment": "22 pages. Comments are welcome!",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We describe the asymptotic behavior of conformal metrics related to the GJMS operator in the null case, as the prescribed Q-curvature $f_0(x) + \\lambda$ gradually changes. We show that if one of the maximum points of $f_0$ is flat up to order $n-1$, the normalized conformal metrics in the lowest energy level will form exactly one spherical bubble as $\\lambda$ approaches zero using higher order Bol's inequality. This generalizes the result of Struwe (JEMS, 2020) in the two-dimensional case to higher dimensions and helps rule out the slow bubble case discussed by Ng\\^o and Zhang (arXiv:1903.12054) to some degree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-24T08:56:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E30",
      "35J60",
      "35J35"
    ],
    "keywords": [
      "asymptotic behavior",
      "null q-curvature",
      "higher order bols inequality",
      "lowest energy level",
      "null case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}