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arXiv · 1502.06812

Free boundary minimal surfaces in the unit 3-ball

Abigail Folha·Frank Pacard·Tatiana Zolotareva
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Abstract

In a recent paper A. Fraser and R. Schoen have proved the existence of free boundary minimal surfaces $\Sigma\_n$ in $B^3$ which have genus $0$ and $n$ boundary components, for all $ n \geq 3$. For large $n$, we give an independent construction of $\Sigma\_n$ and prove the existence of free boundary minimal surfaces $\tilde \Sigma\_n$ in $B^3$ which have genus $1$ and $n$ boundary components. As $n$ tends to infinity, the sequence $\Sigma\_n$ converges to a double copy of the unit horizontal (open) disk, uniformly on compacts of $B^3$ while the sequence $\tilde \Sigma\_n$ converges to a double copy of the unit horizontal (open) punctured disk, uniformly on compacts of $B^3-\{0\}$.

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Abigail Folha, Frank Pacard, Tatiana Zolotareva. 2015-02-24. Free boundary minimal surfaces in the unit 3-ball. https://arxiv.org/abs/1502.06812

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