{
  "id": "1408.0161",
  "version": "v2",
  "published": "2014-08-01T13:00:55.000Z",
  "updated": "2017-01-11T20:34:39.000Z",
  "title": "The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits",
  "authors": [
    "Valentino Tosatti",
    "Ben Weinkove",
    "Xiaokui Yang"
  ],
  "comment": "42 pages, final version to appear in Amer. J. Math",
  "categories": [
    "math.DG"
  ],
  "abstract": "We investigate the Kahler-Ricci flow on holomorphic fiber spaces whose generic fiber is a Calabi-Yau manifold. We establish uniform metric convergence to a metric on the base, away from the singular fibers, and show that the rescaled metrics on the fibers converge to Ricci-flat Kahler metrics. This strengthens previous work of Song-Tian and others. We obtain analogous results for degenerations of Ricci-flat Kahler metrics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-01T13:00:55.000Z",
      "comment": "42 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2017-01-11T20:34:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "53C55",
      "14J32",
      "32Q25",
      "58J35"
    ],
    "keywords": [
      "kähler-ricci flow",
      "ricci-flat metrics",
      "collapsing limits",
      "ricci-flat kahler metrics",
      "holomorphic fiber spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.0161T"
    }
  }
}