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arXiv · 2502.11898

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

Volker Branding·Anna Siffert
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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.

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Volker Branding, Anna Siffert. 2025-02-17. A family of triharmonic maps to spheres in all dimensions greater than two. https://arxiv.org/abs/2502.11898

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