{
  "id": "1505.04869",
  "version": "v1",
  "published": "2015-05-19T04:40:35.000Z",
  "updated": "2015-05-19T04:40:35.000Z",
  "title": "On Feldman-Ilmanen-Knopf conjecture for the blow-up behavior of the Kahler Ricci flow",
  "authors": [
    "Bin Guo",
    "Jian Song"
  ],
  "comment": "24 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We consider the Ricci flow on $\\mathbb{CP}^n$ blown-up at one point starting with any $U(n)$-invariant K\\\"ahler metric. It is known that the K\\\"ahler-Ricci flow must develop Type I singularities. We show that if the total volume does not go to zero at the singular time, then any Type I parabolic blow-up limit of the Ricci flow along the exceptional divisor is the unique $U(n)$-complete shrinking K\\\"ahler-Ricci soliton on $\\mathbb C^n$ blown-up at one point. This establishes the conjecture of Feldman-Ilmanen-Knopf.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-19T04:40:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kahler ricci flow",
      "blow-up behavior",
      "feldman-ilmanen-knopf conjecture",
      "parabolic blow-up limit",
      "exceptional divisor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150504869G"
    }
  }
}