## 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.## References

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## Bibliographic 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), 21-40 - MSC (2000): Primary 30C65, 57R05, 57M60
- DOI: https://doi.org/10.1090/S1088-4173-06-00111-1
- MathSciNet review: 2206314

Dedicated: For Meir, who insisted