# FREE BOUNDARY MINIMAL SURFACES IN THE UNIT 3-BALL

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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https://hal.archives-ouvertes.fr/hal-01119962
Contributor : Tatiana Zolotareva <>
Submitted on : Tuesday, February 24, 2015 - 2:36:49 PM
Last modification on : Thursday, March 5, 2020 - 6:30:27 PM
Document(s) archivé(s) le : Monday, May 25, 2015 - 10:41:04 AM

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FBinB3_FPZ.pdf
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### Identifiers

• HAL Id : hal-01119962, version 1
• ARXIV : 1502.06812

### Citation

Abigail Folha, Frank Pacard, Tatiana Zolotareva. FREE BOUNDARY MINIMAL SURFACES IN THE UNIT 3-BALL. 2015. ⟨hal-01119962⟩

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