{
  "id": "2006.04849",
  "version": "v1",
  "published": "2020-06-08T18:11:41.000Z",
  "updated": "2020-06-08T18:11:41.000Z",
  "title": "The length of the shortest closed geodesic on positively curved 2-spheres",
  "authors": [
    "Ian Adelstein",
    "Franco Vargas Pallete"
  ],
  "comment": "11 pages, 1 figure. Comments are welcome!",
  "categories": [
    "math.DG"
  ],
  "abstract": "We show that the shortest closed geodesic on a 2-sphere with non-negative curvature has length bounded above by three times the diameter. We prove a new isoperimetric inequality for 2-spheres with pinched curvature; this allows us to improve our bound on the length of the shortest closed geodesic in the pinched curvature setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-08T18:11:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C22",
      "53C23"
    ],
    "keywords": [
      "shortest closed geodesic",
      "pinched curvature",
      "isoperimetric inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}