{
  "id": "1912.07711",
  "version": "v1",
  "published": "2019-12-16T21:29:33.000Z",
  "updated": "2019-12-16T21:29:33.000Z",
  "title": "The Length of the Shortest Closed Geodesic on a Surface of Finite Area",
  "authors": [
    "I. Beach",
    "R. Rotman"
  ],
  "comment": "15 pages, 4 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper we prove new upper bounds for the length of a shortest closed geodesic, denoted $l(M)$, on a complete, non-compact Riemannian surface $M$ of finite area $A$. We will show that $l(M) \\leq 4\\sqrt{2A}$ on a manifold with one end, thus improving the prior estimate of C. B. Croke, who first established that $l(M) \\leq 31 \\sqrt{A}$. Additionally, for a surface with at least two ends we show that $l(M) \\leq 2\\sqrt{2A}$, improving the prior estimate of Croke that $l(M) \\leq (12+3\\sqrt{2})\\sqrt{A}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-16T21:29:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "shortest closed geodesic",
      "finite area",
      "prior estimate",
      "non-compact riemannian surface",
      "upper bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}