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math.SP2023
A geometric bound on the lowest magnetic Neumann eigenvalue via the torsion function
Ayman Kachmar, Vladimir Lotoreichik
We obtain an upper bound on the lowest magnetic Neumann eigenvalue of a bounded, convex, smooth, planar domain with moderate intensity of the homogeneous magnetic field. This bound…
math.AP2023
Isoperimetric inequalities for inner parallel curves
Charlotte Dietze, Ayman Kachmar, Vladimir Lotoreichik
We prove weighted isoperimetric inequalities for smooth, bounded, and simply connected domains. More precisely, we show that the moment of inertia of inner parallel curves for doma…