Infinite families of harmonic self-maps of ellipsoids in all dimensions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866915380898824192 |
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| author | Branding, Volker Siffert, Anna |
| author_facet | Branding, Volker Siffert, Anna |
| contents | We prove that for given $k\in\mathbb{N}$, $k\geq 3$, $d\in\mathbb{N}$ and each $a\in\mathbb{R}^{*}$ with \begin{align*} a^2<4d (d+k-2)(k-2)^{-2} \end{align*} the ellipsoid $E_a:=\{x\in\mathbb{R}^k\,\lvert\,a^{-2}x_1^2+x_2^2+\ldots+x_k^2=1\}$ admits infinitely many harmonic self-maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_17240 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Infinite families of harmonic self-maps of ellipsoids in all dimensions Branding, Volker Siffert, Anna Differential Geometry Analysis of PDEs Dynamical Systems We prove that for given $k\in\mathbb{N}$, $k\geq 3$, $d\in\mathbb{N}$ and each $a\in\mathbb{R}^{*}$ with \begin{align*} a^2<4d (d+k-2)(k-2)^{-2} \end{align*} the ellipsoid $E_a:=\{x\in\mathbb{R}^k\,\lvert\,a^{-2}x_1^2+x_2^2+\ldots+x_k^2=1\}$ admits infinitely many harmonic self-maps. |
| title | Infinite families of harmonic self-maps of ellipsoids in all dimensions |
| topic | Differential Geometry Analysis of PDEs Dynamical Systems |
| url | https://arxiv.org/abs/2210.17240 |