{
  "id": "2009.10144",
  "version": "v1",
  "published": "2020-09-21T19:24:57.000Z",
  "updated": "2020-09-21T19:24:57.000Z",
  "title": "Sharp upper bounds on the length of the shortest closed geodesic on complete punctured spheres of finite area",
  "authors": [
    "Antonia Jabbour",
    "Stéphane Sabourau"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We establish sharp universal upper bounds on the length of the shortest closed geodesic on a punctured sphere with three or four ends endowed with a complete Riemannian metric of finite area. These sharp curvature-free upper bounds are expressed in terms of the area of the punctured sphere. In both cases, we describe the extremal metrics, which are modeled on the Calabi-Croke sphere or the tetrahedral sphere. We also extend these optimal inequalities for reversible and non-necessarily reversible Finsler metrics. In this setting, we obtain optimal bounds for spheres with a larger number of punctures. Finally, we present a roughly asymptotically optimal upper bound on the length of the shortest closed geodesic for spheres/surfaces with a large number of punctures in terms of the area.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-21T19:24:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "shortest closed geodesic",
      "sharp upper bounds",
      "complete punctured spheres",
      "finite area",
      "sharp universal upper bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}