{
  "id": "2011.03455",
  "version": "v1",
  "published": "2020-11-06T16:09:51.000Z",
  "updated": "2020-11-06T16:09:51.000Z",
  "title": "Systoles and diameters of hyperbolic surfaces",
  "authors": [
    "Florent Balacheff",
    "Vincent Despré",
    "Hugo Parlier"
  ],
  "comment": "13 pages, 9 figures",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "In this article we explore the relationship between the systole and the diameter of closed hyperbolic orientable surfaces. We show that they satisfy a certain inequality, which can be used to deduce that their ratio has a (genus dependent) upper bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-06T16:09:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic surfaces",
      "closed hyperbolic orientable surfaces",
      "genus dependent",
      "upper bound",
      "inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}