The existence of quasimeromorphic mappings in dimension 3

Saucan, Emil

doi:10.1090/S1088-4173-06-00111-1

The existence of quasimeromorphic mappings in dimension 3
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by Emil Saucan

Conform. Geom. Dyn. 10 (2006), 21-40

DOI: https://doi.org/10.1090/S1088-4173-06-00111-1

Published electronically: March 1, 2006

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Abstract:

We prove that a Kleinian group $G$ acting on $\mathbb {H}^{3}$ admits a non-constant $G$-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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