Free boundary minimal surfaces in the unit 3-ball

By Abigail Folha, Frank Pacard, Tatiana Zolotareva. 2015

66 citations recorded by the source corpus.

A. Fraser and R. Schoen proved the existence of free boundary minimal surfaces $$\Sigma _n$$Σn in $$B^3$$B3 which have genus 0 and n boundary components, for all $$ n \ge 3$$n≥3. For large n, we give an independent construction of $$\Sigma _n$$Σn and prove the existence of free boundary minimal surfaces $${{\tilde{\Sigma }}}_n$$Σ~n in $$B^3$$B3 which have genus 1 and n boundary components. As n tends to infinity, the sequence $$\Sigma _n$$Σn converges to a double copy of the unit horizontal (open) disk, uniformly on compacts of $$B^3$$B3 while the sequence $${{\tilde{\Sigma }}}_n$$Σ~n converges to a double copy of the unit horizontal (open) punctured disk, uniformly on compacts of $$B^3 \setminus \{0\}$$B3\{0}.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9f20acbe4a34c74485f93ebdee2d155ca90061b3

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Minimal Surfaces in the Round Three‐Sphere by Doubling the Equatorial Two‐Sphere, II (2014, background): “Doubling constructions for free boundary minimal surfaces in the Euclidean three-ball have also recently been carried out [5, 16].”
Free boundary minimal surfaces in the unit ball : recent advances and open questions (2019, unknown): “The first such construction is given by Folha, Pacard and Zolotareva in [20].”
Compactness analysis for free boundary minimal hypersurfaces (2017, background): “In the Euclidean ball, Fraser and Schoen have obtained free boundary minimal surfaces with genus zero and any number of boundary components larger than one [17], while Folha, Pacard and Zolotareva [13] have obtained free boundary minimal surfaces with genus zero or one and any sufficiently large num”
Index estimates for free boundary minimal hypersurfaces (2016, methodology): “In particular, the examples constructed by Fraser and Schoen [9], which have genus zero and an arbitrary number of boundary components, and the examples constructed by Folha, Pacard and Zolotareva [4], which have genus one and an arbitrarily large number of boundary components, have their Morse indi”