Publication

Preprint

Date

July, 2024

Links

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 $< k$ \emph{in distributional sense}. This complements known examples of such kind of homeomorphisms whose gradient has rank $<k$ \emph{almost everywhere}.