Infinite families of harmonic self-maps of spheres

Abstract

For each of the spheres ${\mathbb{S}}^n$, $n\ge 5$, we construct a new infinite family of harmonic self-maps, and prove that their members have Brouwer degree $\pm 1$ or $\pm 3$. These self-maps are obtained by solving a singular boundary value problem.

arXiv commentRevised version; to appear in Journal of Differential Equations