The holomorphic-disk area conjecture for Lagrangians in balls

Let $B^{2n}(a)$ be the symplectic ball of capacity $a$, let $L$ be a Lagrangian submanifold in $B^{2n}(a)$, and let $J$ be an admissible almost-complex structure. Holomorphic-disk area conjecture. Every Lagrangian $L$ in $B^{2n}(a)$ bounds $J$-holomorphic disks of area at most $a/2$ for all admissible $J$ whenever $n>1$. This conjecture concerns uniform upper bounds on the areas of $J$-holomorphic disks bounded by Lagrangians in symplectic balls; its status is not specified in the source.