Free boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial disc
Nikolaos Kapouleas, Martin Man‐chun Li
Abstract
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 disc. 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 by using the min-max method.
Topics & Concepts
Minimal surfaceHelicoidCoaxialBall (mathematics)MathematicsEuclidean geometryMathematical analysisGeometryUnit sphereBoundary (topology)Constant-mean-curvature surfaceMean curvatureComputer scienceCurvatureMean curvature flowTelecommunicationsGeometric Analysis and Curvature FlowsNonlinear Partial Differential EquationsPoint processes and geometric inequalities