{
  "id": "1004.3826",
  "version": "v3",
  "published": "2010-04-22T01:38:08.000Z",
  "updated": "2011-05-19T13:28:18.000Z",
  "title": "Sufficient conditions for open manifolds to be diffeomorphic to Euclidean spaces",
  "authors": [
    "Kei Kondo",
    "Minoru Tanaka"
  ],
  "comment": "This version 3 (13 pages, no figures) is a version to appear in Differential Geometry and its Applications",
  "journal": "Differential Geometry and its Applications, vol. 29 (2011) 597-605",
  "doi": "10.1016/j.difgeo.2011.04.040",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let M be a complete non-compact connected Riemannian n-dimensional manifold. We first prove that, for any fixed point p in M, the radial Ricci curvature of M at p is bounded from below by the radial curvature function of some non-compact n-dimensional model. Moreover, we then prove, without the pointed Gromov-Hausdorff convergence theory, that, if model volume growth is sufficiently close to 1, then M is diffeomorphic to Euclidean n-dimensional space. Hence, our main theorem has various advantages of the Cheeger-Colding diffeomorphism theorem via the Euclidean volume growth. Our main theorem also contains a result of do Carmo and Changyu as a special case.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-05-19T13:28:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C21"
    ],
    "keywords": [
      "open manifolds",
      "euclidean spaces",
      "sufficient conditions",
      "diffeomorphic",
      "non-compact connected riemannian n-dimensional manifold"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.3826K"
    }
  }
}