Nitsche's uniqueness conjecture for free boundary minimal annuli

Let $\mathbb{B}^3$ be the unit ball in Euclidean three-space, and let a free boundary minimal annulus be an embedded minimal annulus whose boundary lies on $\partial\mathbb{B}^3$ and meets it orthogonally. The critical catenoid is the rotationally symmetric free boundary minimal annulus in $\mathbb{B}^3$. Nitsche's uniqueness conjecture. Every embedded free boundary minimal annulus in $\mathbb{B}^3$ is congruent to the critical catenoid. This conjecture is a uniqueness problem for free boundary minimal surfaces; the supplied text attributes its resolution to Fraser and Li, so it is recorded as solved.