An upper bound on the growth of Dirichlet tilings of hyperbolic spaces

Abstract

It is shown that the growth rate [Formula: see text] of any [Formula: see text] faces Dirichlet tiling of [Formula: see text] is at most [Formula: see text], for an [Formula: see text], depending only on [Formula: see text] and [Formula: see text]. We do not know if there is a universal [Formula: see text], such that [Formula: see text] upperbounds the growth rate for any [Formula: see text]-regular tiling, when [Formula: see text]?