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The Cheeger constants of random Belyi surfaces

Differential Geometry 2023-02-21 v2 Geometric Topology Spectral Theory

Abstract

Brooks and Makover developed a combinatorial model of random hyperbolic surfaces by gluing certain hyperbolic ideal triangles. In this paper we show that for any ϵ>0\epsilon>0, as the number of ideal triangles goes to infinity, a generic hyperbolic surface in Brooks-Makover's model has Cheeger constant less than 32π+ϵ\frac{3}{2\pi}+\epsilon.

Keywords

Cite

@article{arxiv.2204.09853,
  title  = {The Cheeger constants of random Belyi surfaces},
  author = {Yang Shen and Yunhui Wu},
  journal= {arXiv preprint arXiv:2204.09853},
  year   = {2023}
}

Comments

International Mathematics Research Notices (IMRN), to appear