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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.06708 |
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Table of Contents:
- We construct an explicit family of stable proper weak biharmonic maps from the unit ball $B^m$, $m\geq 5$, to Euclidean spheres. To the best of the authors knowledge this is the first example of a stable proper weak biharmonic map from at compact domain. To achieve our result we first establish the second variation formula of the bienergy for maps from the unit ball into a Euclidean sphere. Employing this result, we examine the stability of the proper weak biharmonic maps $q:B^m\to\mathbb{S}^{m^{\ell}}$, $m,\ell\in\mathbb{N}$ with $\ell\leq m$, which we recently constructed in \cite{BS25} and thus deduce the existence of an explicit family of stable proper biharmonic maps to Euclidean spheres.