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Conformal Geometry and Dynamics

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The existence of quasimeromorphic mappings in dimension 3

Author: Emil Saucan
Journal: Conform. Geom. Dyn. 10 (2006), 21-40
MSC (2000): Primary 30C65, 57R05, 57M60
Published electronically: March 1, 2006
MathSciNet review: 2206314
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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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Additional Information

Emil Saucan
Affiliation: Departments of Mathematics and Electrical Engineering, Technion, Haifa, Israel

Keywords: Automorphic quasimeromorphic mapping, fat triangulation
Received by editor(s): December 1, 2003
Received by editor(s) in revised form: January 20, 2006
Published electronically: March 1, 2006
Dedicated: For Meir, who insisted
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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