Uniform $W^{2,m}$ approximation of almost isometric maps

This paper shows that an almost-isometric Sobolev map from a Lipschitz subset of an oriented manifold $M$ into another oriented manifold $N$ can be approximated by a map of class $C^{1,α}$, with a universal bound on the $W^{2,m}$ norm, for any $m\in(1,\infty)$. This, in turn, implies a universal bou