Essential spectral geometry of the Maxwell system in unbounded domains

We analyse the essential spectrum of ${\mathcal M} = {\operatorname{curl}} {\operatorname{curl}}$ acting on divergence-free vector fields in unbounded domains of $\mathbb{R}^3$. We show that $σ_e({\mathcal M}) = [0,+\infty)$ in quasi-conical domains and $σ_e({\mathcal M}) \neq \emptyset$ in quasi-cy