Published Paper

Inserted: 12 oct 2025
Last Updated: 26 may 2026

Journal: Math. Nachr.
Volume: 299
Number: 1230–1240
Pages: 11
Year: 2026
Doi: 10.1002/mana.70136

Abstract:

We investigate how the lowest eigenvalue of a magnetic Laplacian depends on the geometry of a planar domain with a disk shaped hole, where the magnetic field is generated by a singular flux. Under Dirichlet boundary conditions on the inner boundary and Neumann boundary conditions on the outer boundary, we show that this eigenvalue is maximized when the domain is an annulus, for a fixed area and magnetic flux. As consequences, we establish geometric inequalities for eigenvalues in settings with both singular and localized magnetic fields. We also propose a conjecture for a general optimality result and establish its validity for large magnetic fluxes.