论嵌入单元 3 球的零属自由边界极小曲面的面积

The Journal of Geometric Analysis Pub Date : 2024-06-27 DOI:10.1007/s12220-024-01726-2

Peter McGrath, Jiahua Zou

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引用次数: 0

摘要

我们证明了嵌入单位 3 球的每个非平面零属自由边界极小曲面的面积小于其径向投影到 \({\mathbb {S}}^2\) 的面积。这个不等式在渐近上是尖锐的，我们证明了任何饱和它的曲面序列都会弱收敛于\({\mathbb {S}}^2\), 作为电流和变分曲面。

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

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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The Journal of Geometric Analysis

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