arXiv Open Access 2023

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

Peter McGrath Jiahua Zou

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Abstrak

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.

Topik & Kata Kunci

math.DG

Penulis (2)

Peter McGrath

Jiahua Zou

Format Sitasi

APA MLA BibTeX

McGrath, P., Zou, J. (2023). On the Areas of Genus Zero Free Boundary Minimal Surfaces Embedded in the Unit $3$-ball. https://arxiv.org/abs/2301.01892

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓