{
  "id": "math/0402238",
  "version": "v1",
  "published": "2004-02-14T15:31:02.000Z",
  "updated": "2004-02-14T15:31:02.000Z",
  "title": "Convergence of a Kähler-Ricci flow",
  "authors": [
    "Natasa Sesum"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper we prove that for a given K\\\"ahler-Ricci flow with uniformly bounded Ricci curvatures in an arbitrary dimension, for every sequence of times $t_i$ converging to infinity, there exists a subsequence such that $(M,g(t_i + t))\\to (Y,\\bar{g}(t))$ and the convergence is smooth outside a singular set (which is a set of codimension at least 4) to a solution of a flow. We also prove that in the case of complex dimension 2, without any curvature assumptions we can find a subsequence of times such that we have a convergence to a K\\\"ahler-Ricci soliton, away from finitely many isolated singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-14T15:31:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44"
    ],
    "keywords": [
      "kähler-ricci flow",
      "convergence",
      "arbitrary dimension",
      "curvature assumptions",
      "subsequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2238S"
    }
  }
}