The existence of quasimeromorphic mappings in dimension 3
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Abstract:
We prove that a Kleinian group $G$ acting on $\mathbb {H}^{3}$ 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.References

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Additional Information
 Emil Saucan
 Affiliation: Departments of Mathematics and Electrical Engineering, Technion, Haifa, Israel
 Email: semil@tx.technion.ac.il, semil@ee.technion.ac.il
 Received by editor(s): December 1, 2003
 Received by editor(s) in revised form: January 20, 2006
 Published electronically: March 1, 2006
 © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.  Journal: Conform. Geom. Dyn. 10 (2006), 2140
 MSC (2000): Primary 30C65, 57R05, 57M60
 DOI: https://doi.org/10.1090/S1088417306001111
 MathSciNet review: 2206314
Dedicated: For Meir, who insisted