{
  "id": "math/0702257",
  "version": "v2",
  "published": "2007-02-09T18:05:07.000Z",
  "updated": "2007-08-22T06:03:39.000Z",
  "title": "A survey on the Kähler-Ricci flow and Yau's uniformization conjecture",
  "authors": [
    "Albert Chau",
    "Luen-Fai Tam"
  ],
  "comment": "Theorem 4.4 has been improved. Theorem 6.6 has been added",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "Yau's uniformization conjecture states: a complete noncompact K\\\"ahler manifold with positive holomorphic bisectional curvature is biholomorphic to $\\ce^n$. The K\\\"ahler-Ricci flow has provided a powerful tool in understanding the conjecture, and has been used to verify the conjecture in several important cases. In this article we present a survey of the K\\\"ahler-Ricci flow with focus on its application to uniformization. Other interesting methods and results related to the study of Yau's conjecture are also discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-08-22T06:03:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C55",
      "35K90"
    ],
    "keywords": [
      "kähler-ricci flow",
      "yaus uniformization conjecture states",
      "positive holomorphic bisectional curvature",
      "yaus conjecture",
      "complete noncompact"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2257C"
    }
  }
}