{
  "id": "0910.1053",
  "version": "v2",
  "published": "2009-10-06T16:39:40.000Z",
  "updated": "2009-12-17T05:09:11.000Z",
  "title": "Gradient estimates for the heat equation under the Ricci flow",
  "authors": [
    "Mihai Bailesteanu",
    "Xiaodong Cao",
    "Artem Pulemotov"
  ],
  "comment": "21 pages, 2 figures",
  "journal": "Journal of Functional Analysis 258 (2010), pages 3517-3542",
  "doi": "10.1016/j.jfa.2009.12.003",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "The paper considers a manifold $M$ evolving under the Ricci flow and establishes a series of gradient estimates for positive solutions of the heat equation on $M$. Among other results, we prove Li-Yau-type inequalities in this context. We consider both the case where $M$ is a complete manifold without boundary and the case where $M$ is a compact manifold with boundary. Applications of our results include Harnack inequalities for the heat equation on $M$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-12-17T05:09:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heat equation",
      "ricci flow",
      "gradient estimates",
      "harnack inequalities",
      "complete manifold"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.1053B"
    }
  }
}