Sharp upper bounds for Steklov eigenvalues of a hypersurface of revolution with two boundary components in Euclidean space
| Autor: | Tschanz, Léonard |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Ann. Math. Qu\'ebec 48, 489 (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s40316-024-00225-8 |
| Popis: | 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. Comment: 29 pages, 7 figures |
| Databáze: | arXiv |
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