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This research explores how strong magnetic fields affect the symmetry of optimal domains for magnetic eigenvalues.

On Shape Optimization with Large Magnetic Fields in Two Dimensions

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Analysis demonstrates symmetry in optimal domains for magnetic eigenvalues in two dimensions, suggesting implications for shape design.

This research explores how strong magnetic fields affect the symmetry of optimal domains for magnetic eigenvalues.
Established asymptotic bounds on magnetic eigenvalues.
Analyzed eigenvalues of magnetic Dirichlet Laplacians in bounded simply-connected planar domains.
Derived results for magnetic Dirichlet Laplacians on rectangles.
Investigated the magnetic Dirac operator with infinite mass boundary conditions.
Provided a new estimate for the torsion function on rectangles.
Optimal domains exhibit greater symmetry under strong magnetic fields.
When eigenvalues for non-disk domains are smaller than those for disks, Fraenkel asymmetry approaches zero.
Results indicate similar patterns for rectangles and smooth domains.

Lotoreichik et al. (2026) studied this question.

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