The first Aharonov-Bohm eigenvalue on simply connected surfaces satisfies isoperimetric inequalities and is maximized by centered geodesic disks or antipodal punctures.
On the isoperimetric inequality for the first positive Neumann eigenvalue on the sphere
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abstract
We prove that the geodesic disks are the unique maximisers of the first non-trivial Neumann eigenvalue among all simply connected domains of the sphere $\mathbb S^2$ with fixed area.
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2026 1verdicts
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Isoperimetric inequalities and sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces
The first Aharonov-Bohm eigenvalue on simply connected surfaces satisfies isoperimetric inequalities and is maximized by centered geodesic disks or antipodal punctures.