Upper bounds for the Steklov eigenvalues of warped products
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917151730827264 |
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| author | Brisson, Jade Colbois, Bruno Girouard, Alexandre Gittins, Katie |
| author_facet | Brisson, Jade Colbois, Bruno Girouard, Alexandre Gittins, Katie |
| contents | We obtain upper bounds for the Steklov eigenvalues of warped products $Ω\times_hΣ$, where $Ω$ is a compact Riemannian manifold with boundary and $Σ$ is a closed Riemannian manifold. These bounds involve the volume of $Ω$ and of $\partialΩ$ as well as the eigenvalues of the Laplace operator on the fiber $Σ$ and the $L^p$-norm of the warping function $h$. The bounds are very different depending on the dimension $n$ of the fiber $Σ$ and the value of $p$. In some cases, we obtain optimal upper bounds and stability estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15416 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Upper bounds for the Steklov eigenvalues of warped products Brisson, Jade Colbois, Bruno Girouard, Alexandre Gittins, Katie Spectral Theory Differential Geometry 35P15, 58C40 We obtain upper bounds for the Steklov eigenvalues of warped products $Ω\times_hΣ$, where $Ω$ is a compact Riemannian manifold with boundary and $Σ$ is a closed Riemannian manifold. These bounds involve the volume of $Ω$ and of $\partialΩ$ as well as the eigenvalues of the Laplace operator on the fiber $Σ$ and the $L^p$-norm of the warping function $h$. The bounds are very different depending on the dimension $n$ of the fiber $Σ$ and the value of $p$. In some cases, we obtain optimal upper bounds and stability estimates. |
| title | Upper bounds for the Steklov eigenvalues of warped products |
| topic | Spectral Theory Differential Geometry 35P15, 58C40 |
| url | https://arxiv.org/abs/2512.15416 |