Stable proper biharmonic maps in Euclidean spheres
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913933764329472 |
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| author | Branding, Volker Siffert, Anna |
| author_facet | Branding, Volker Siffert, Anna |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06708 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable proper biharmonic maps in Euclidean spheres Branding, Volker Siffert, Anna Differential Geometry Analysis of PDEs 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. |
| title | Stable proper biharmonic maps in Euclidean spheres |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2507.06708 |