General magnetic eigenvalue disk-minimizer conjecture

Let $n\geq2$, let $B$ be a constant magnetic field, and let $\lambda_n(\Omega,B)$ denote the $n$th eigenvalue of the magnetic Dirichlet Laplacian on a bounded open domain $\Omega\subset\mathbb{R}^2$ with $|\Omega|=1$. Let $D$ be a disk with $|D|=1$. Magnetic disk-minimizer conjecture. If $B\geq2\pi n$, then

$$\lambda_n(\Omega,B)\geq\lambda_n(D,B)$$

for every such $\Omega$. Numerical results for $n=2,3,4,5,6,7$ motivate the conjecture, but the general assertion remains open.