Upper bound for Steklov eigenvalues of warped products with fiber of dimension 2
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916310136389632 |
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| author | Brisson, Jade Colbois, Bruno |
| author_facet | Brisson, Jade Colbois, Bruno |
| contents | In this note, we investigate the Steklov spectrum of the warped product $[0,L]\times_h Σ$ equipped with the metric $dt^2+h(t)^2g_Σ$, where $Σ$ is a compact surface. We find sharp upper bounds for the Steklov eigenvalues in terms of the eigenvalues of the Laplacian on $Σ$. We apply our method to the case of metric of revolution on the 3-dimensional ball and we obtain a sharp estimate on the spectral gap between two consecutive Steklov eigenvalues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13620 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Upper bound for Steklov eigenvalues of warped products with fiber of dimension 2 Brisson, Jade Colbois, Bruno Spectral Theory Differential Geometry 58J50, 58C40, 35P15 In this note, we investigate the Steklov spectrum of the warped product $[0,L]\times_h Σ$ equipped with the metric $dt^2+h(t)^2g_Σ$, where $Σ$ is a compact surface. We find sharp upper bounds for the Steklov eigenvalues in terms of the eigenvalues of the Laplacian on $Σ$. We apply our method to the case of metric of revolution on the 3-dimensional ball and we obtain a sharp estimate on the spectral gap between two consecutive Steklov eigenvalues. |
| title | Upper bound for Steklov eigenvalues of warped products with fiber of dimension 2 |
| topic | Spectral Theory Differential Geometry 58J50, 58C40, 35P15 |
| url | https://arxiv.org/abs/2403.13620 |