{
  "id": "1504.05873",
  "version": "v1",
  "published": "2015-04-22T16:42:34.000Z",
  "updated": "2015-04-22T16:42:34.000Z",
  "title": "An Upper bound on the growth of Dirichlet tilings of hyperbolic spaces",
  "authors": [
    "Itai Benjamini",
    "Tsachik Gelander"
  ],
  "categories": [
    "math.GR",
    "math.MG"
  ],
  "abstract": "It is shown that the growth rate $(\\lim_r |B(r)|^{1/r})$ of any $k$ faces Dirichlet tiling of the real hyperbolic space $\\mathbb{H}^d, d>2,$ is at most $k-1-\\epsilon$, for an $\\epsilon > 0$, depending only on $k$ and $d$. We don't know if there is a universal $\\epsilon_u > 0$, such that $k-1-\\epsilon_u$ upperbounds the growth rate for any $k$-regular tiling, when $ d > 2$?",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-22T16:42:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "upper bound",
      "growth rate",
      "real hyperbolic space",
      "faces dirichlet tiling",
      "upperbounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150405873B"
    }
  }
}