Nitsche–Fraser–Li conjecture for free boundary minimal annuli

Let $\mathbb{B}^3$ be the Euclidean unit ball, and let an embedded free boundary minimal annulus be an embedded minimal annulus whose boundary meets $\partial\mathbb{B}^3$ orthogonally. The Nitsche–Fraser–Li conjecture. The unique embedded free boundary minimal annulus in $\mathbb{B}^3$ is the critical catenoid. This is the free-boundary analogue of the Lawson conjecture for embedded minimal tori. Uniqueness is known among rotationally symmetric embedded minimal annuli, while uniqueness without the symmetry assumption remains open.