Prescription of the Robin spectrum
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918080503873536 |
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| author | He, Xiang Wang, Zuoqin |
| author_facet | He, Xiang Wang, Zuoqin |
| contents | Let $M$ be a compact connected smooth manifold with smooth boundary, and let $ρ$ be a positive continuous function on the boundary which is served as the Robin parameter. In this paper, we study three problems concerning the prescription of finite Robin spectrum: (1) Prescribing finitely many Robin eigenvalues and the volume. (2) Within a fixed conformal class, prescribing the multiplicities of finitely many Robin eigenvalues. (3) Within a fixed conformal class, prescribing finitely many distinct Robin eigenvalues and the volume. A key step in our method is to solve the corresponding problems for the Dirichlet spectrum. As a consequence, we also obtain analogous results for the Dirichlet case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Prescription of the Robin spectrum He, Xiang Wang, Zuoqin Spectral Theory 58C40, 58J50, 81Q35, 30F45 Let $M$ be a compact connected smooth manifold with smooth boundary, and let $ρ$ be a positive continuous function on the boundary which is served as the Robin parameter. In this paper, we study three problems concerning the prescription of finite Robin spectrum: (1) Prescribing finitely many Robin eigenvalues and the volume. (2) Within a fixed conformal class, prescribing the multiplicities of finitely many Robin eigenvalues. (3) Within a fixed conformal class, prescribing finitely many distinct Robin eigenvalues and the volume. A key step in our method is to solve the corresponding problems for the Dirichlet spectrum. As a consequence, we also obtain analogous results for the Dirichlet case. |
| title | Prescription of the Robin spectrum |
| topic | Spectral Theory 58C40, 58J50, 81Q35, 30F45 |
| url | https://arxiv.org/abs/2503.01451 |