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Free-boundary minimal surfaces with connected boundary in the $3$-ball by tripling the equatorial disc
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In the Euclidean unit three-ball, we construct compact, embedded, two-sided free boundary minimal surfaces with connected boundary and prescribed high genus, by a gluing construction tripling the equatorial disc. Aside from the equatorial disc itself, these are the first examples in the three-ball of compact free boundary minimal surfaces with connected boundary.
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Cited by 2 Pith papers
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Under positive scalar curvature and mean-convex boundary, a Morse index bound bounds area, genus, boundary components, and total curvature of free boundary minimal surfaces, while topology or area bounds alone fail to...
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