The Existence of Quasimeromorphic Mappings in Dimension 3

We prove that a Kleinian group G acting on H3 admits a nonconstant 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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