{
  "id": "1210.3083",
  "version": "v2",
  "published": "2012-10-10T23:10:40.000Z",
  "updated": "2012-10-15T19:48:46.000Z",
  "title": "Time-analyticity of solutions to the Ricci flow",
  "authors": [
    "Brett Kotschwar"
  ],
  "comment": "34 pages; v2: some typos corrected",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper, we prove that if $g(t)$ is a smooth, complete solution to the Ricci flow of uniformly bounded curvature on $M\\times[0, \\Omega]$, then the correspondence $t\\mapsto g(t)$ is real-analytic at each $t_0\\in (0, \\Omega)$. The analyticity is a consequence of classical Bernstein-type estimates on the temporal and spatial derivatives of the curvature tensor, which we further use to show that, under the above global hypotheses, for any $x_0\\in M$ and $t_0\\in (0, \\Omega)$, there exist local coordinates $x = x^i$ on a neighborhood $U\\subset M$ of $x_0$ in which the representation $g_{ij}(x, t)$ of the metric is real-analytic in both $x$ and $t$ on some cylinder $U\\times (t_0 -\\epsilon, t_0 + \\epsilon)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-15T19:48:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "58J35"
    ],
    "keywords": [
      "ricci flow",
      "time-analyticity",
      "real-analytic",
      "complete solution",
      "local coordinates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.3083K"
    }
  }
}