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Optimization problems for magnetic ground states on surfaces

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GSTW05 - Emerging Horizons in Geometric Spectral Theory: an ECRs workshop

In this talk we consider the first eigenvalue of the magnetic Laplacian with zero magnetic field on surfaces. For simply connected domains of the $2$-sphere we show a Szeg\”o-type isoperimetric inequality holding without any restriction on the area of the domain. Moreover, we show that the optimal configuration of the two magnetic poles maximising the first eigenvalue of $\mathbb S^2$ occurs when they are antipodal. We also show geometric inequalities for the first eigenvalue on Riemannian surfaces under an upper bound on the Gaussian curvature, and prove that a Hersch-type upper bound cannot hold in the magnetic case. This is a joint work with L. Provenzano and A. Savo

This talk is part of the Isaac Newton Institute Seminar Series series.

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Mott Seminar Room, Cavendish Laboratory, Department of Physics Johnson Matthey Lecture Theatre, Department of Chemical Engineering & Biotechnology, Philippa Fawcett Drive, Cambridge CB3 0AS Average on weekdays: 9010.2324633 kWh

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