4 problems

Absence of embedded eigenvalues conjecture. The point spectrum of the perturbed magnetic Stark Hamiltonian is empty:

Let $L$ be the periodic Schrödinger operator in equation (1), and let $\sigma(L)$ denote its spectrum. A solution is called well-decaying at infinity if it has the decay property i…

Localized-perturbation conjecture. If, for some $\lambda$ in the interior of a spectral band, there is an irreducible component $A$ of the Fermi surface with…

Let $K(r)$ denote the radial curvature of an asymptotically flat manifold, and consider the curvature condition in part (1) of Theorem 2, which permits an arbitrary finite set of e…