Free-boundary minimal surfaces with connected boundary in the $3$-ball by tripling the equatorial disc

Abstract

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.

33 pages, 1 figure, with minor improvements over first version