Sharp upper bounds for Steklov eigenvalues of a hypersurface of revolution with two boundary components in Euclidean space
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913542230245376 |
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| author | Tschanz, Léonard |
| author_facet | Tschanz, Léonard |
| contents | We investigate the question of sharp upper bounds for the Steklov eigenvalues of a hypersurface of revolution of the Euclidean space with two boundary components isometric to two copies of $\mathbb{S}^{n-1}$. For the case of the first non zero Steklov eigenvalue, we give a sharp upper bound $B_n(L)$ (that depends only on the dimension $n \ge 3$ and the meridian length $L>0$) which is reached by a degenerated metric $g^*$, that we compute explicitly. We also give a sharp upper bound $B_n$ which depends only on $n$. Our method also permits us to prove some stability properties of these upper bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11964 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sharp upper bounds for Steklov eigenvalues of a hypersurface of revolution with two boundary components in Euclidean space Tschanz, Léonard Differential Geometry Spectral Theory We investigate the question of sharp upper bounds for the Steklov eigenvalues of a hypersurface of revolution of the Euclidean space with two boundary components isometric to two copies of $\mathbb{S}^{n-1}$. For the case of the first non zero Steklov eigenvalue, we give a sharp upper bound $B_n(L)$ (that depends only on the dimension $n \ge 3$ and the meridian length $L>0$) which is reached by a degenerated metric $g^*$, that we compute explicitly. We also give a sharp upper bound $B_n$ which depends only on $n$. Our method also permits us to prove some stability properties of these upper bounds. |
| title | Sharp upper bounds for Steklov eigenvalues of a hypersurface of revolution with two boundary components in Euclidean space |
| topic | Differential Geometry Spectral Theory |
| url | https://arxiv.org/abs/2302.11964 |