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arXiv · 2604.11718

Isoperimetric inequalities and sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces

Marco Michetti·Luigi Provenzano·Alessandro Savo
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Abstract

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.

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Marco Michetti, Luigi Provenzano, Alessandro Savo. 2026-04-29. Isoperimetric inequalities and sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces. https://arxiv.org/abs/2604.11718

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