{
  "id": "1107.0606",
  "version": "v3",
  "published": "2011-07-04T12:35:20.000Z",
  "updated": "2011-08-23T13:22:55.000Z",
  "title": "How to produce a Ricci Flow via Cheeger-Gromoll exhaustion",
  "authors": [
    "Esther Cabezas-Rivas",
    "Burkhard Wilking"
  ],
  "comment": "42 pages, Added: a) example of an immortal solution which flows from bounded to unbounded curvature in finite time, b) long time analysis of the Ricci flow",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We prove short time existence for the Ricci flow on open manifolds of nonnegative complex sectional curvature. We do not require upper curvature bounds. By considering the doubling of convex sets contained in a Cheeger-Gromoll convex exhaustion and solving the singular initial value problem for the Ricci flow on these closed manifolds, we obtain a sequence of closed solutions of the Ricci flow with nonnegative complex sectional curvature which subconverge to a solution of the Ricci flow on the open manifold. Furthermore, we find an optimal volume growth condition which guarantees long time existence, and we give an analysis of the long time behaviour of the Ricci flow. Finally, we construct an explicit example of an immortal nonnegatively curved solution of the Ricci flow with unbounded curvature for all time.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-08-23T13:22:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C44",
      "53C20"
    ],
    "keywords": [
      "ricci flow",
      "cheeger-gromoll exhaustion",
      "nonnegative complex sectional curvature",
      "guarantees long time existence",
      "optimal volume growth condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.0606C"
    }
  }
}