Title: Free Boundary Minimal Surfaces in the Unit Three-Ball via Desingularization of the Critical Catenoid and the Equatorial Disk,
Abstract: We construct a new family of high genus examples of free boundary minimal
surfaces in the Euclidean unit 3-ball by desingularizing the intersection of a
coaxial pair of a critical catenoid and an equatorial disk. The surfaces are
constructed by singular perturbation methods and have three boundary
components. They are the free boundary analogue of the Costa-Hoffman-Meeks
surfaces and the surfaces constructed by Kapouleas by desingularizing coaxial
catenoids and planes. It is plausible that the minimal surfaces we constructed
here are the same as the ones obtained recently by Ketover using the min-max
method.