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We prove that the area of each nonflat genus zero free boundary minimalsurface embedded in the unit $3$-ball is less than the area of its radialprojection to $\mathbb{S}^2$. The inequality is asymptotically sharp, and weprove any sequence of surfaces saturating it converges weakly to$\mathbb{S}^2$, as currents and as varifolds.

On the Areas of Genus Zero Free Boundary Minimal Surfaces Embedded in the Unit $3$-ball