Several isoperimetric inequalities of Dirichlet and Neumann eigenvalues of the Witten-Laplacian
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909645377896448 |
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| author | Chen, Ruifeng Mao, Jing |
| author_facet | Chen, Ruifeng Mao, Jing |
| contents | In this paper, by mainly using the rearrangement technique and suitably constructing trial functions, under the constraint of fixed weighted volume, we can successfully obtain several isoperimetric inequalities for the first and the second Dirichlet eigenvalues, the first nonzero Neumann eigenvalue of the Witten-Laplacian on bounded domains in space forms. These spectral isoperimetric inequalities extend those classical ones (i.e. the Faber-Krahn inequality, the Hong-Krahn-Szegő inequality and the Szegő-Weinberger inequality) of the Laplacian. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_08075 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Several isoperimetric inequalities of Dirichlet and Neumann eigenvalues of the Witten-Laplacian Chen, Ruifeng Mao, Jing Analysis of PDEs Differential Geometry 35P15, 35J10, 35J15 In this paper, by mainly using the rearrangement technique and suitably constructing trial functions, under the constraint of fixed weighted volume, we can successfully obtain several isoperimetric inequalities for the first and the second Dirichlet eigenvalues, the first nonzero Neumann eigenvalue of the Witten-Laplacian on bounded domains in space forms. These spectral isoperimetric inequalities extend those classical ones (i.e. the Faber-Krahn inequality, the Hong-Krahn-Szegő inequality and the Szegő-Weinberger inequality) of the Laplacian. |
| title | Several isoperimetric inequalities of Dirichlet and Neumann eigenvalues of the Witten-Laplacian |
| topic | Analysis of PDEs Differential Geometry 35P15, 35J10, 35J15 |
| url | https://arxiv.org/abs/2403.08075 |