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The Existence of Quasimeromorphic Mappings

Emil Saucan
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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.

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Emil Saucan. 2004-04-30. The Existence of Quasimeromorphic Mappings. https://arxiv.org/abs/math/0405002

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