Some conformal properties of \(p\)-harmonic maps and a regularity for sphere-valued \(p\)-harmonic maps
Let \(u : M \to N\) be a smooth map between Riemannian manifolds and \(p\) a real number, \(1 < p < +\infty\). We say that \(u\) is a \(p\)-harmonic map if it is a critical point of the \(p\)-energy functional \(\int_ \Omega | du|^ p\) for every compact domain \(\Omega \subset M\). The aim of this paper is to study conformal properties of \(p\)-harmonic maps and the regularity problem for sphere-valued \(p\)-harmonic maps. It should be mentioned that this article -- which is a good reference for people wanting to learn the standard Riemannian geometric facts about \(p\)-harmonic maps -- has some overlapping with an article of \textit{P. Baird} and \textit{S. Gudmundsson} [Math. Ann. 294, No. 4, 611-624 (1992; Zbl 0757.53031)].
scientific article; zbMATH DE number 711437