Sharp estimates for the Robin Laplacian under a perimeter constraint in hyperbolic space
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912905921822720 |
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| author | Chen, Daguang Li, Shan |
| author_facet | Chen, Daguang Li, Shan |
| contents | In this paper, we establish a lower bound, in terms of the isoperimetric deficit, for the first eigenvalue of the Robin Laplacian with negative boundary parameter on horospherically convex bounded domains in the hyperbolic space. This implies that the geodesic ball maximizes this eigenvalue among all such domains, thereby providing a partial resolution to an open problem posed by Celentano, Krejčiřík and Lotoreichik in \cite{CKL26}. Furthermore, we derive upper bounds for the first eigenvalue of the Robin Laplacian with positive boundary parameter on horospherically convex bounded domains in the hyperbolic space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07510 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp estimates for the Robin Laplacian under a perimeter constraint in hyperbolic space Chen, Daguang Li, Shan Differential Geometry Analysis of PDEs 35P15, 58J50, 52A55 In this paper, we establish a lower bound, in terms of the isoperimetric deficit, for the first eigenvalue of the Robin Laplacian with negative boundary parameter on horospherically convex bounded domains in the hyperbolic space. This implies that the geodesic ball maximizes this eigenvalue among all such domains, thereby providing a partial resolution to an open problem posed by Celentano, Krejčiřík and Lotoreichik in \cite{CKL26}. Furthermore, we derive upper bounds for the first eigenvalue of the Robin Laplacian with positive boundary parameter on horospherically convex bounded domains in the hyperbolic space. |
| title | Sharp estimates for the Robin Laplacian under a perimeter constraint in hyperbolic space |
| topic | Differential Geometry Analysis of PDEs 35P15, 58J50, 52A55 |
| url | https://arxiv.org/abs/2602.07510 |