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arXiv · 2301.01892

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

Peter McGrath·Jiahua Zou
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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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Peter McGrath, Jiahua Zou. 2023-01-05. On the Areas of Genus Zero Free Boundary Minimal Surfaces Embedded in the Unit $3$-ball. https://arxiv.org/abs/2301.01892

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