Sobolev mappings: Lipschitz density is not a bi-Lipschitz invariant of   the target
  We study a question of density of Lipschitz mappings in the Sobolev class of mappings from a closed manifold into a singular space. The main result of the paper shows that if we change the metric in the target space to a bi-Lipschitz equivalent one, than the property of the density of Lipschitz mappings may be lost. 
Piotr Hajlasz