The Existence of Quasimeromorphic Mappings

Abstract

We prove that a Kleinian group $G$ acting upon ${\mathbb{H}}^n$ admits a non-constant $G$-automorphic function, even if it has torsion elements, provided that the orders of the elliptic (torsion) elements are uniformly bounded. This is accomplished by developing a technique for mashing distinct fat triangulations while preserving fatness.

13 pages, 2 figures