Abstract
We prove that a Kleinian group G G acting on H 3 \mathbb {H}^{3} admits a non-constant G G -automorphic function, even if it has torsion elements, provided that the orders of the elliptic elements are uniformly bounded. This is accomplished by developing a method for meshing distinct fat triangulations which is fatness preserving. We further show how to adapt the proof to higher dimensions.
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