Note on a Theorem of Munkres

We prove that given a 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 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 As an application we prove the existence of G-automorphic quasimeromorphic mappings, where G is a Kleinian group acting onDedicated to the memory of Robert BrooksThis paper represents part of the authors Ph.D. thesis written under the supervision of Prof. Uri Srebro.