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 , as the number of ideal triangles goes to infinity, a generic hyperbolic surface in Brooks-Makover's model has Cheeger constant less than .
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