  We show that for any $k$ and $s > \frac{k+1}{k+2}$ there exist neither
$W^{s,\frac{k}{s}}$-Sobolev nor $C^s$-H\"older homeomorphisms from the disk
$\mathbb{B}^n$ into $\mathbb{R}^N$ whose gradient has rank $< k$ in
distributional sense. This complements known examples of such kind of
homeomorphisms whose gradient has rank $<k$ almost everywhere.
