Cieliebak–Mohnke extremal Lagrangian torus conjecture for the unit ball

Let an extremal Lagrangian torus in $(\bar{B}^{2n}(1),\omega_{\mathrm{std}})$ mean a Lagrangian torus whose symplectic energy attains the relevant Lagrangian capacity. Cieliebak–Mohnke's conjecture. Every extremal Lagrangian torus in the standard symplectic unit ball $(\bar{B}^{2n}(1),\omega_{\mathrm{std}})$ lies entirely on the boundary $\partial B^{2n}(1)$. The conjecture is known in dimension four by work of Dimitroglou Rizell, and is proved in all dimensions in the present paper.