The Clifford torus energy minimization conjecture

Let $\Sigma$ be a Lagrangian torus in $\mathbb{C}P^2$, with energy functional

$$E(\Sigma)=\frac{1}{2}\int_{\Sigma}V\,dx\wedge dy=A(\Sigma)+\frac{1}{8}W(\Sigma),$$

where $A(\Sigma)$ is its area and $W(\Sigma)$ is the integral of the squared norm of its mean curvature vector. Let $\Sigma_{Cl}$ be the Clifford torus, whose energy is

$$E(\Sigma_{Cl})=\frac{4\pi^2}{3\sqrt{3}}.$$

Clifford torus energy minimization conjecture. The minimum of the energy functional is attained on the Clifford torus.

This conjecture proposes that the Clifford torus minimizes the geometric energy among Lagrangian tori in $\mathbb{C}P^2$; the supplied source does not state whether it has been resolved.