On the Effectless Cut Method for Laplacian Eigenvalues in any dimensions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914437454102528 |
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| author | Amato, Vincenzo Gavitone, Nunzia de Giovanni, Francesca |
| author_facet | Amato, Vincenzo Gavitone, Nunzia de Giovanni, Francesca |
| contents | In this paper, we study the optimization of the first Laplacian eigenvalue on axisymmetric doubly connected domains under positive Robin boundary conditions. Under additional geometric constraints, we prove that spherical shells maximize this eigenvalue. Our approach combines known isoperimetric inequalities for mixed Laplacian eigenvalues with a higher-dimensional extension of the effectless cut technique introduced by Hersch to study multiply connected membranes of given area fixed along their boundaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00976 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Effectless Cut Method for Laplacian Eigenvalues in any dimensions Amato, Vincenzo Gavitone, Nunzia de Giovanni, Francesca Spectral Theory Analysis of PDEs 35P05, 35P15 In this paper, we study the optimization of the first Laplacian eigenvalue on axisymmetric doubly connected domains under positive Robin boundary conditions. Under additional geometric constraints, we prove that spherical shells maximize this eigenvalue. Our approach combines known isoperimetric inequalities for mixed Laplacian eigenvalues with a higher-dimensional extension of the effectless cut technique introduced by Hersch to study multiply connected membranes of given area fixed along their boundaries. |
| title | On the Effectless Cut Method for Laplacian Eigenvalues in any dimensions |
| topic | Spectral Theory Analysis of PDEs 35P05, 35P15 |
| url | https://arxiv.org/abs/2604.00976 |