{
  "id": "2005.09196",
  "version": "v1",
  "published": "2020-05-19T03:42:12.000Z",
  "updated": "2020-05-19T03:42:12.000Z",
  "title": "A new uniform lower bound on Weil-Petersson distance",
  "authors": [
    "Yunhui Wu"
  ],
  "comment": "Any comments are welcome",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "In this paper we study the injectivity radius based at a fixed point along Weil-Petersson geodesics. We show that the square root of the injectivity radius based at a fixed point is $ 0.3884$-Lipschitz on Teichm\\\"uller space endowed with the Weil-Petersson metric. As an application we reprove that the square root of the systole function is uniformly Lipschitz on Teichm\\\"uller space endowed with the Weil-Petersson metric, where the Lipschitz constant can be chosen to be $0.5492$. Applications to asymptotic geometry of moduli space of Riemann surfaces for large genus will also be discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-19T03:42:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniform lower bound",
      "weil-petersson distance",
      "weil-petersson metric",
      "injectivity radius",
      "square root"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}