{
  "id": "1001.2278",
  "version": "v2",
  "published": "2010-01-13T19:24:15.000Z",
  "updated": "2010-05-31T17:31:49.000Z",
  "title": "Curvature, sphere theorems, and the Ricci flow",
  "authors": [
    "S. Brendle",
    "R. M. Schoen"
  ],
  "comment": "This is an invited contribution for the Bulletin of the AMS",
  "categories": [
    "math.DG",
    "math.AP",
    "math.GT",
    "math.MG"
  ],
  "abstract": "This is a survey paper focusing on the interplay between the curvature and topology of a Riemannian manifold. The first part of the paper provides a background discussion, aimed at non-experts, of Hopf's pinching problem and the Sphere Theorem. In the second part, we sketch the proof of the Differentiable Sphere Theorem, and discuss various related results. These results employ a variety of methods, including geodesic and minimal surface techniques as well as Hamilton's Ricci flow.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-31T17:31:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimal surface techniques",
      "hamiltons ricci flow",
      "survey paper",
      "first part",
      "background discussion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}