A bound for diameter of arithmetic hyperbolic orbifolds

Mikhail Belolipetsky

A bound for diameter of arithmetic hyperbolic orbifolds

Metric Geometry 2021-02-25 v3 Geometric Topology

Authors: Mikhail Belolipetsky

Abstract

Let $O$ be a closed $n$ -dimensional arithmetic (real or complex) hyperbolic orbifold. We show that the diameter of $O$ is bounded above by $\frac{c_1\log vol(O) + c_2}{h(O)},$ where $h(O)$ is the Cheeger constant of $O$ , $vol(O)$ is its volume, and constants $c_1$ , $c_2$ depend only on $n$ .

Keywords

simplicial volume hyperbolic geometry

Cite

@article{arxiv.2001.07520,
  title  = {A bound for diameter of arithmetic hyperbolic orbifolds},
  author = {Mikhail Belolipetsky},
  journal= {arXiv preprint arXiv:2001.07520},
  year   = {2021}
}

Comments

9 pages, final version, to appear in Geom. Dedicata. The paper uses and extends to the complex hyperbolic orbifolds some results of arXiv:math/0612132 and arXiv:1811.05280

A bound for diameter of arithmetic hyperbolic orbifolds

Abstract

Keywords

Cite

Comments

Related papers