Eigenvalue lower bounds through a generalized inradius
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912601581027328 |
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| author | Frank, Rupert L. Laptev, Ari Suragan, Durvudkhan |
| author_facet | Frank, Rupert L. Laptev, Ari Suragan, Durvudkhan |
| contents | Lieb has shown a lower bound on the smallest Dirichlet eigenvalue of the Laplace operator in terms of a generalized inradius. We derive similar bounds for Robin eigenvalues, for eigenvalues of the polyharmonic operator and the sub-Laplacian on the Heisenberg group. We propose a method based on Hardy inequalities that is different from Lieb's approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18878 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eigenvalue lower bounds through a generalized inradius Frank, Rupert L. Laptev, Ari Suragan, Durvudkhan Spectral Theory Analysis of PDEs Functional Analysis 35P15, 58J50 Lieb has shown a lower bound on the smallest Dirichlet eigenvalue of the Laplace operator in terms of a generalized inradius. We derive similar bounds for Robin eigenvalues, for eigenvalues of the polyharmonic operator and the sub-Laplacian on the Heisenberg group. We propose a method based on Hardy inequalities that is different from Lieb's approach. |
| title | Eigenvalue lower bounds through a generalized inradius |
| topic | Spectral Theory Analysis of PDEs Functional Analysis 35P15, 58J50 |
| url | https://arxiv.org/abs/2509.18878 |