2 problems

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The planar annulus conjecture for the first magnetic Steklov eigenvalue
Planar annulus conjecture. Is it true that every doubly connected planar domain $\Omega$ has
Conjectureopenmagnetic-stecklov-problem planar-domains spectral-geometryarXiv posted 2 days ago
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The critical catenoid conjecture for the second magnetic Steklov eigenvalue
Critical catenoid conjecture. The critical catenoid maximizes $\bar\sigma_2(\Sigma,\nu)$ among all annuli, for every $\nu\in\mathbb R$ .
Conjectureopenmagnetic-stecklov-problem riemannian-geometry spectral-geometryarXiv posted 2 days ago

The planar annulus conjecture for the first magnetic Steklov eigenvalue