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On the Areas of Genus Zero Free Boundary Minimal Surfaces Embedded in the Unit $3$-ball
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math.DG
keywords
areaballboundaryembeddedfreegenusmathbbminimal
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abstract
We prove that the area of each nonflat genus zero free boundary minimal surface embedded in the unit $3$-ball is less than the area of its radial projection to $\mathbb{S}^2$. The inequality is asymptotically sharp, and we prove any sequence of surfaces saturating it converges weakly to $\mathbb{S}^2$, as currents and as varifolds.
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