{
  "id": "2104.10630",
  "version": "v1",
  "published": "2021-04-21T16:48:30.000Z",
  "updated": "2021-04-21T16:48:30.000Z",
  "title": "Dynamical (in)stability of Ricci-flat ALE metrics along Ricci flow",
  "authors": [
    "Alix Deruelle",
    "Tristan Ozuch"
  ],
  "comment": "56 pages, comments welcome!",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study the stability and instability of ALE Ricci-flat metrics around which a Lojasiewicz inequality is satisfied for a variation of Perelman's $\\lambda$-functional adapted to the ALE situation and denoted $\\lambda_{\\operatorname{ALE}}$. This functional was introduced by the authors in a recent work and it has been proven that it satisfies a good enough Lojasiewicz inequality at least in neighborhoods of integrable ALE Ricci-flat metrics in dimension larger than or equal to 5.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-21T16:48:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ricci-flat ale metrics",
      "ricci flow",
      "lojasiewicz inequality",
      "integrable ale ricci-flat metrics",
      "dimension larger"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}