Infinite families of harmonic self-maps of spheres

TL;DR

This paper constructs infinite families of harmonic self-maps on spheres of dimension five and higher, with degrees ±1 or ±3, by solving a singular boundary value problem, expanding understanding of harmonic maps.

Contribution

It introduces new infinite families of harmonic self-maps for spheres of dimension five and above, with specific Brouwer degrees, via solving a novel singular boundary value problem.

Findings

Constructed infinite families of harmonic self-maps for spheres $ ext{S}^n$, n≥5.

Members have Brouwer degree ±1 or ±3.

Maps obtained through solving a singular boundary value problem.

Abstract

For each of the spheres $\mathbb{S}^{n}$, $n\geq 5$, we construct a new infinite family of harmonic self-maps, and prove that their members have Brouwer degree $\pm1$ or $\pm3$. These self-maps are obtained by solving a singular boundary value problem.