Affiliation:
1. Yau Mathematical Sciences Center and Department of Mathematical Sciences , Tsinghua University, Beijing 100084, China
Abstract
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 $\epsilon>0$, as the number of ideal triangles goes to infinity, a generic hyperbolic surface in Brooks–Makover’s model has Cheeger constant less than $\frac {3}{2\pi }+\epsilon $.
Publisher
Oxford University Press (OUP)
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