{
  "id": "2003.01326",
  "version": "v1",
  "published": "2020-03-03T04:22:19.000Z",
  "updated": "2020-03-03T04:22:19.000Z",
  "title": "On the escape rate of geodesic loops in an open manifold with nonnegative Ricci curvature",
  "authors": [
    "Jiayin Pan"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "A consequence of the Cheeger-Gromoll splitting theorem states that for any open manifold $(M,x)$ of nonnegative Ricci curvature, if all the minimal geodesic loops at $x$ that represent elements of $\\pi_1(M,x)$ are contained in a bounded ball, then $\\pi_1(M,x)$ is virtually abelian. We generalize the above result: if these minimal representing geodesic loops of $\\pi_1(M,x)$ escape from any bounded metric balls at a sublinear rate with respect to their lengths, then $\\pi_1(M,x)$ is virtually abelian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-03T04:22:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonnegative ricci curvature",
      "open manifold",
      "escape rate",
      "cheeger-gromoll splitting theorem states",
      "minimal geodesic loops"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}