Critical lengths of Steklov eigenvalues of hypersurfaces of revolution in Euclidean space
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912069698191360 |
|---|---|
| author | Métras, Antoine Tschanz, Léonard |
| author_facet | Métras, Antoine Tschanz, Léonard |
| contents | We study the Steklov problem on hypersurfaces of revolution with two boundary components in Euclidean space. In a recent article, the phenomenon of critical length, at which a Steklov eigenvalue is maximized, was exhibited and multiple questions were raised. In this article, we conjecture that, in any dimension, there is a finite number of infinite critical length. To investigate this, we develop an algorithm to efficiently perform numerical experiments, providing support to our conjecture. Furthermore, we prove the conjecture in dimension $n = 3$ and $n = 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10743 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Critical lengths of Steklov eigenvalues of hypersurfaces of revolution in Euclidean space Métras, Antoine Tschanz, Léonard Spectral Theory We study the Steklov problem on hypersurfaces of revolution with two boundary components in Euclidean space. In a recent article, the phenomenon of critical length, at which a Steklov eigenvalue is maximized, was exhibited and multiple questions were raised. In this article, we conjecture that, in any dimension, there is a finite number of infinite critical length. To investigate this, we develop an algorithm to efficiently perform numerical experiments, providing support to our conjecture. Furthermore, we prove the conjecture in dimension $n = 3$ and $n = 4$. |
| title | Critical lengths of Steklov eigenvalues of hypersurfaces of revolution in Euclidean space |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2401.10743 |