2 problems

Let $d=3$, and let $\Gamma$ be a periodic curve for which a decomposition into translates of a suitable period cell $\mathcal{P}$ satisfying hypothesis (c) does not exist, for exam…

Let $\Gamma$ be a smooth curve that is a local deformation of a straight line, with curvature $\kappa$, and let $\alpha$ be the coupling strength in the leaky-wire Hamiltonian. Def…