{
  "id": "1611.00925",
  "version": "v1",
  "published": "2016-11-03T09:25:45.000Z",
  "updated": "2016-11-03T09:25:45.000Z",
  "title": "On the analytic systole of Riemannian surfaces of finite type",
  "authors": [
    "Werner Ballmann",
    "Henrik Matthiesen",
    "Sugata Mondal"
  ],
  "comment": "35 pages, 1 figure",
  "categories": [
    "math.DG"
  ],
  "abstract": "In our previous work we introduced, for a Riemannian surface $S$, the quantity $ \\Lambda(S):=\\inf_F\\lambda_0(F)$, where $\\lambda_0(F)$ denotes the first Dirichlet eigenvalue of $F$ and the infimum is taken over all compact subsurfaces $F$ of $S$ with smooth boundary and abelian fundamental group. A result of Brooks implies $\\Lambda(S)\\ge\\lambda_0(\\tilde{S})$, the bottom of the spectrum of the universal cover $\\tilde{S}$. In this paper, we discuss the strictness of the inequality. Moreover, in the case of curvature bounds, we relate $\\Lambda(S)$ with the systole, improving a result by the last named author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-03T09:25:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemannian surface",
      "finite type",
      "analytic systole",
      "first dirichlet eigenvalue",
      "abelian fundamental group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}