{
  "id": "0809.3963",
  "version": "v2",
  "published": "2008-09-23T16:50:09.000Z",
  "updated": "2009-01-12T22:19:33.000Z",
  "title": "Remarks on Kahler Ricci Flow",
  "authors": [
    "Xiuxiong Chen",
    "Bing Wang"
  ],
  "comment": "We note an overlap with the paper of Rubinstein [Ru1]. We add more reference",
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "abstract": "We study some estimates along the Kahler Ricci flow on Fano manifolds. Using these estimates, we show the convergence of Kahler Ricci flow directly if the $\\alpha$-invariant of the canonical class is greater than $\\frac{n}{n+1}$. Applying these convergence theorems, we can give a flow proof of Calabi conjecture on such Fano manifolds. In particular, the existence of Kahler Einstein metrics on a lot of Fano surfaces can be proved by flow method. Note that this geometric conclusion (based on the same assumption) was established earlier via elliptic method by G. Tian. However, a new proof based on Kahler Ricci flow should be still interesting in its own right.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-01-12T22:19:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44"
    ],
    "keywords": [
      "fano manifolds",
      "kahler einstein metrics",
      "elliptic method",
      "kahler ricci flow",
      "geometric conclusion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.3963C"
    }
  }
}