Of the non-existence of BLD mappings between manifolds

In this thesis we study existence ofbounded length distortion(BLD) mappings between manifolds by mimicing the proof of a Varopoulos type result. The restraints mimic the volume-growth invariants of the case of quasiregular maps between Riemannian manifolds. Our basic method is to construct invariants from the 'coarse volumes' of covering spaces, which can be in some situations compared with the combined growth of the original manifold and its fundamental group.