Abstract
A. Fraser and R. Schoen proved the existence of free boundary minimal surfaces \(\Sigma _n\) in \(B^3\) which have genus 0 and n boundary components, for all \( n \ge 3\). 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 \(B^3 \setminus \{0\}\).
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F. Pacard and T. Zolotareva are partially supported by the ANR-2011-IS01-002 Grant.
T. Zolotareva is partially supported by the FMJH through the ANR-10-CAMP-0151-02 Grant.
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Folha, A., Pacard, F. & Zolotareva, T. Free boundary minimal surfaces in the unit 3-ball. manuscripta math. 154, 359–409 (2017). https://doi.org/10.1007/s00229-017-0924-9
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DOI: https://doi.org/10.1007/s00229-017-0924-9