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

Abstract

We present a construction method for triharmonic maps to spheres. In particular, we show that for any $m\in \mathbb{N}$ with $m\ge 3$ 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.