On the minimality of the radial singularity in nematic liquid crystals

We show that the map $u_*\colon B_1\subset\mathbb R^3\to\mathbb S^2$, $x\mapsto x/|x|$, minimizes the anisotropic energy \begin{align*} \int_{B_1} \Big( k_1(\mathrm{div}\, u)^2+k_2 (u\cdot \mathrm{curl}\, u)^2 +k_3 |u\times\mathrm{curl}\, u|^2 \Big) \, dx, \end{align*} among $\mathbb S^2$-valued map