5 problems

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…

Let $\Omega$ be a regular domain in $\mathbb{R}^2$, let $A_0$ be a magnetic potential whose magnetic field is constant and has norm $1$, and let $\lambda^{\rm DN}(bA_0,\Omega)$ den…

Let $\Omega$ be a regular domain in $\mathbb{R}^2$, and let $A_0$ be a magnetic potential whose magnetic field is constant and has norm $1$. Let $\Lambda_{bA_0}$ be the associated…

Let $\mu_{1}$ be the first band function, let $\xi_{0}$ denote its minimum point, and write $\mu_{1}^{(3)}(\xi_{0})$ for its third derivative there. Third-derivative conjecture. ……

Let $\zeta_{1}(\tau)$ be the lowest band function associated with the three-dimensional magnetic Hamiltonian with axisymmetric potential. The preceding analysis shows that…