4 problems

Let the optimal domain be a domain in $\mathbb{R}^3$ minimizing the first eigenvalue of the curl operator under the relevant volume constraint. A spheromak is a torus whose central…

Consider the first positive eigenvalue of the curl operator on a domain in $\mathbb{R}^3$, subject to the tangential boundary condition … A spheromak is a sphere whose south and no…

Let $M$ range over the closed hyperbolic orientable three-manifolds in the volume interval considered in the source, and consider the minimisers for the curl operator among manifol…

Let $M$ be a compact connected three-manifold with non-empty boundary, and let the first non-null eigenvalue of the curl operator be considered on $M$. Gerner's conjecture. The mul…