{
  "id": "1702.07033",
  "version": "v1",
  "published": "2017-02-22T22:45:29.000Z",
  "updated": "2017-02-22T22:45:29.000Z",
  "title": "Length of a shortest closed geodesic in manifolds of dimension four",
  "authors": [
    "Nan Wu",
    "Zhifei Zhu"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we show that for any closed 4-dimensional simply-connected Riemannian manifold $M$ with Ricci curvature $|Ric|>3$, volume $vol(M)>v>0$, and diameter $diam(M)<D$, the length of a shortest closed geodesic is bounded by a function $F(v,D)$ which only depends on $v$ and $D$. The proofs of our result is based on a recent theorem of diffeomorphism finiteness of the manifolds satisfying the above conditions proven by J. Cheeger and A. Naber.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-22T22:45:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C23"
    ],
    "keywords": [
      "shortest closed geodesic",
      "simply-connected riemannian manifold",
      "ricci curvature",
      "conditions proven",
      "diffeomorphism finiteness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}