{
  "id": "0904.2604",
  "version": "v2",
  "published": "2009-04-16T23:21:53.000Z",
  "updated": "2009-07-01T00:13:22.000Z",
  "title": "Sphere Theorems in Geometry",
  "authors": [
    "S. Brendle",
    "R. M. Schoen"
  ],
  "comment": "Some typos corrected; to appear in Surveys in Differential Geometry",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this paper, we give a survey of various sphere theorems in geometry. These include the topological sphere theorem of Berger and Klingenberg as well as the differentiable version obtained by the authors. These theorems employ a variety of methods, including geodesic and minimal surface techniques as well as Hamilton's Ricci flow. We also obtain here new results concerning complete manifolds with pinched curvature.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-07-01T00:13:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimal surface techniques",
      "results concerning complete manifolds",
      "hamiltons ricci flow",
      "topological sphere theorem",
      "theorems employ"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.2604B"
    }
  }
}