Harmonic Self-maps of $\mbox{SU}(3)$

TL;DR

This paper constructs an infinite family of harmonic self-maps of SU(3) with non-trivial Brouwer degree by solving a singular boundary value problem, expanding understanding of harmonic maps in Lie groups.

Contribution

It introduces a method to generate infinitely many harmonic self-maps of SU(3) with non-trivial degree through solving a specific boundary value problem.

Findings

Existence of infinitely many harmonic self-maps of SU(3)

Construction method via singular boundary value problem

Maps have non-trivial Brouwer degree

Abstract

By constructing solutions of a singular boundary value problem we prove the existence of a countably infinite family of harmonic self-maps of $\mbox{SU}(3)$ with non-trivial, i.e. $\neq 0,\pm 1$, Brouwer degree.