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SUMMARY:Optimization problems for magnetic ground states on surfaces - Mar
 co Michetti (Chalmers University of Technology)
DTSTART:20260206T121500Z
DTEND:20260206T124500Z
UID:TALK239581@talks.cam.ac.uk
DESCRIPTION:In this talk we consider the first eigenvalue of the magnetic 
 Laplacian with zero magnetic field on surfaces. For simply connected domai
 ns of the $2$-sphere we show a Szeg\\"o-type isoperimetric inequality hold
 ing without any restriction on the area of the domain. Moreover\, we show 
 that the optimal configuration of the two magnetic poles maximising the fi
 rst eigenvalue of $\\mathbb S^2$ occurs when they are antipodal. We also s
 how 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 wi
 th L. Provenzano and A. Savo
LOCATION:Seminar Room 1\, Newton Institute
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