Strong diamagnetism conjecture for magnetic Dirichlet-to-Neumann ground states

Let $\Omega\subset\mathbb{R}^d$ be any bounded set, and let the magnetic field be constant. Denote by $\lambda^{\rm DN}(A,\Omega)$ the ground-state energy of the magnetic Dirichlet-to-Neumann operator associated with a magnetic potential $A$. Strong diamagnetism conjecture. The magnetic ground-state energy satisfies a strict strong-diamagnetism property for constant magnetic fields, as asserted in the source.

The preceding discussion establishes the ordinary diamagnetic inequality $\lambda^{\rm DN}(A,\Omega)\geq\lambda^{\rm DN}(0,\Omega)$, while the source separately refers to strong diamagnetism and to equality cases treated in earlier work. The exact strictness formulation is not included in the supplied statement.