Quantitative Magnetic Isoperimetric Inequality
Spectral Theory
2023-05-15 v1 Mathematical Physics
math.MP
Abstract
In 1996 Erdoes 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.
Cite
@article{arxiv.2305.07431,
title = {Quantitative Magnetic Isoperimetric Inequality},
author = {Rohan Ghanta and Lukas Junge and Leo Morin},
journal= {arXiv preprint arXiv:2305.07431},
year = {2023}
}