On the magnetic Dirichlet to Neumann operator on the disk -- strong diamagnetism and strong magnetic field limit--

Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operator on the disk tends to $+\mathrm{\infty }$ as the magnetic field tends to $+\mathrm{\infty }$. This is an important step towards the analysis of the curvature effect in the case of general domains in ${\mathbb{R}}^2$.