Upper bound for Steklov eigenvalues of warped products with fiber of dimension 2
| Autor: | Brisson, Jade, Colbois, Bruno |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this note, we investigate the Steklov spectrum of the warped product $[0,L]\times_h \Sigma$ equipped with the metric $dt^2+h(t)^2g_\Sigma$, where $\Sigma$ is a compact surface. We find sharp upper bounds for the Steklov eigenvalues in terms of the eigenvalues of the Laplacian on $\Sigma$. 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. Comment: Theorems 1.3 and 1.4 have been incorporated in the preprint arXiv:2403.13426v2 [math.SP] by J. Brisson, B. Colbois and K. Gittins, since the method used in both are similar. The other results of this preprint will be presented in a more general context, in a forthcoming paper |
| Databáze: | arXiv |
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