Isoperimetric inequalities and sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces
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| Format: | Preprint |
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2026
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| _version_ | 1866914516043825152 |
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| author | Michetti, Marco Provenzano, Luigi Savo, Alessandro |
| author_facet | Michetti, Marco Provenzano, Luigi Savo, Alessandro |
| contents | We consider the first eigenvalue of the magnetic Laplacian with zero magnetic field on simply connected compact surfaces and we establish isoperimetric inequalities and upper bounds in terms of a bound on the gaussian curvature. As a corollary, we prove that among all simply connected spherical domains of fixed area, the first eigenvalue is maximal for a geodesic disk with the pole of the magnetic potential at its center; also, for the sphere punctured at two points, the first eigenvalue is maximal when the punctures are antipodal. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_11718 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Isoperimetric inequalities and sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces Michetti, Marco Provenzano, Luigi Savo, Alessandro Spectral Theory Differential Geometry 35P15, 49Rxx, 58J50, 81Q10 We consider the first eigenvalue of the magnetic Laplacian with zero magnetic field on simply connected compact surfaces and we establish isoperimetric inequalities and upper bounds in terms of a bound on the gaussian curvature. As a corollary, we prove that among all simply connected spherical domains of fixed area, the first eigenvalue is maximal for a geodesic disk with the pole of the magnetic potential at its center; also, for the sphere punctured at two points, the first eigenvalue is maximal when the punctures are antipodal. |
| title | Isoperimetric inequalities and sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces |
| topic | Spectral Theory Differential Geometry 35P15, 49Rxx, 58J50, 81Q10 |
| url | https://arxiv.org/abs/2604.11718 |