A family of triharmonic maps to spheres in all dimensions greater than two

TL;DR

This paper introduces a construction method for triharmonic maps from Euclidean spaces to spheres in all dimensions greater than two, including explicit examples and a deformation approach for proper r-harmonic maps.

Contribution

It provides a general construction technique for triharmonic maps in all dimensions greater than two and introduces a deformation method for proper r-harmonic maps between spheres.

Findings

Existence of triharmonic maps from ^m into spheres for all m .

Construction method based on eigenmap deformation.

Explicit examples of proper r-harmonic maps.

Abstract

We present a construction method for triharmonic maps to spheres. In particular, we show that for any $m\in\mathbb{N}$ with $m\geq 3$ there exists a triharmonic map from $\mathbb{R}^m\setminus\{0\}$ into a round sphere. In addition, we provide a construction method for proper $r$-harmonic maps between spheres based on a suitable deformation of eigenmaps.