Hyperbolic Coxeter groups of minimal growth rates in higher dimensions

2021/11/17 by Naomi Bredon, Bredon, Naomi
Computer Science · Mathematics · #11R06 #20F55 #22E40 #26A12 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2111.09208

openalex publication_date 2021/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The cusped hyperbolic n-orbifolds of minimal volume are well known for n ≤ 9. Their fundamental groups are related to the Coxeter n-simplex groups Γ_n listed in Table 1. In this work, we prove that Γ_n has minimal growth rate among all non-cocompact Coxeter groups of finite covolume in \hboxIsom\mathbb Hⁿ. In this way, we extend previous results of Floyd for n = 2 and of Kellerhals for n = 3 respectively. Our proof is a generalisation of the methods developed in [2] for the cocompact case.

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