Examples of $p$-harmonic maps

We construct explicit examples of $p$-harmonic maps $u:{\mathbb{R}}^n\to {\mathbb{R}}^N$. These are more irregular than the previously known examples and thus provide new upper bounds for the regularity of $p$-harmonic maps, including the case of $\mathrm{\infty }$-harmonic maps. To optimize our approach, we utilize solutions of the Hurwitz problem from algebra.