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arxiv: 2603.04236 · v3 · submitted 2026-03-04 · 🧮 math.SP · math.AP· math.DG

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On the isoperimetric inequality for the first positive Neumann eigenvalue on the sphere

Luigi Provenzano , Alessandro Savo
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classification 🧮 math.SP math.APmath.DG
keywords eigenvaluefirstneumannsphereareaconnecteddisksdomains
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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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  1. Isoperimetric inequalities and sharp upper bounds for Aharonov-Bohm eigenvalues on surfaces

    math.SP 2026-04 unverdicted novelty 7.0

    The first Aharonov-Bohm eigenvalue on simply connected surfaces satisfies isoperimetric inequalities and is maximized by centered geodesic disks or antipodal punctures.