5 problems

For $0<\alpha\leq\pi$, let … and let $\operatorname{P}_{1,U_\alpha}=-(\nabla-i\mathbf{A}_0)^2$ be the magnetic Neumann Laplacian on $U_\alpha$. Write…

Let $S_{\alpha}$ be the planar sector of opening $\alpha\in(0,2\pi)$, and let $E(S_{\alpha},1)$ denote the bottom of the spectrum of the Neumann magnetic Laplacian on $S_{\alpha}$…

Magnetic energy convergence conjecture. The convergence

Let $\Omega$ be a domain, let $B_0$ tend to infinity, and suppose that … where $\lambda_1(\Omega,B_0)$ is the lowest eigenvalue of the magnetic Laplacian with constant magnetic fie…

Let a domain be equipped with its Laplacian, and consider spectral partitions of the domain. Allow a number of Aharonov–Bohm flux lines, with both their number and positions subjec…