Mediterranean Journal of Mathematics

, Volume 2, Issue 2, pp 215–229 | Cite as

Note on a Theorem of Munkres

Original Paper

Abstract.

We prove that given a \(\mathcal{C}^\infty \) Riemannian manifold with boundary, having a finite number of compact boundary components, any fat triangulation of the boundary can be extended to the whole manifold. We also show that this result extends to \(\mathcal{C}^1 \) manifolds and to embedded PL manifolds of dimensions 2, 3 and 4. We employ these results to prove that manifolds of the types above admit quasimeromorphic mappings onto \(\widehat{\mathbb{R}^n }.\) As an application we prove the existence of G-automorphic quasimeromorphic mappings, where G is a Kleinian group acting on \(\mathbb{H}^n .\)

Mathematics Subject Classification (2000).

Primary 57R05 Secondary 57M60 30C65 

Keywords.

Fat triangulation quasimeromorphic mapping 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Department of Mathematics, Technion, Haifa and Software Engineering DepartmentOrt Braude CollegeKarmielIsrael

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