Quantitative magnetic isoperimetric inequality
Rohan Ghanta, Lukas Junge, Léo Morin · Journal of Spectral Theory · 2024
In 1996 Erdős showed that among planar domains of fixed area, the smallest principal eigenvalue of the Dirichlet Laplacian with a constant magnetic field is uniquely achieved on the disk. We establish a quantitative version of this inequality, with an explicit remainder term depending on the field strength that measures how much the domain deviates from the disk.