3 problems

Unique stable BD profile conjecture. For $K>4$, the $\mathbf{P}^b$-$BD$-$\mathbf{P}^t$ configuration is the unique stable mixed three-dimensional critical point on $V_K$.

BD minimiser conjecture. The $\mathbf{P}^b$-$BD$-$\mathbf{P}^t$ configuration is the unique reduced Landau-de Gennes minimiser for small $h$ and remains potentially stable for all…

Planarity conjecture. After the field is removed, the director remains in the plane of the polygon.