Geodesic
Hyperbolic Coxeter groups of minimal growth rates in higher dimensions
Canadian mathematical bulletin, Tome 66 (2023) no. 1, pp. 232-242

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DOI

The cusped hyperbolic n-orbifolds of minimal volume are well known for $n\leq 9$. Their fundamental groups are related to the Coxeter n-simplex groups $\Gamma _{n}$. In this work, we prove that $\Gamma _{n}$ has minimal growth rate among all non-cocompact Coxeter groups of finite covolume in $\textrm{Isom}\mathbb H^{n}$. In this way, we extend previous results of Floyd for $n=2$ and of Kellerhals for $n=3$, respectively. Our proof is a generalization of the methods developed together with Kellerhals for the cocompact case.
DOI : 10.4153/S000843952200025X
Mots-clés : Coxeter group, growth rate, hyperbolic Coxeter polyhedron, affine vertex stabilizer 
Bredon, Naomi. Hyperbolic Coxeter groups of minimal growth rates in higher dimensions. Canadian mathematical bulletin, Tome 66 (2023) no. 1, pp. 232-242. doi: 10.4153/S000843952200025X
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     title = {Hyperbolic {Coxeter} groups of minimal growth rates in higher dimensions},
     journal = {Canadian mathematical bulletin},
     pages = {232--242},
     year = {2023},
     volume = {66},
     number = {1},
     doi = {10.4153/S000843952200025X},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S000843952200025X/}
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