Examples of $p$-harmonic maps

TL;DR

This paper constructs explicit, irregular examples of p-harmonic maps from R^n to R^N, providing new insights into their regularity bounds, especially for the case of infinity-harmonic maps, by leveraging algebraic solutions from the Hurwitz problem.

Contribution

It introduces a novel method for constructing irregular p-harmonic maps using algebraic solutions, expanding the known examples and improving regularity bounds.

Findings

New explicit examples of p-harmonic maps with irregular behavior

Enhanced upper bounds for regularity of p-harmonic maps

Application of algebraic solutions from the Hurwitz problem

Abstract

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 $\infty$-harmonic maps. To optimize our approach, we utilize solutions of the Hurwitz problem from algebra.