Free boundary minimal surfaces with connected boundary and arbitrary genus

Abstract

We employ min-max techniques to show that the unit ball in ${\mathbb{R}}^3$ contains embedded free boundary minimal surfaces with connected boundary and arbitrary genus.

References in corpus (3)

• Free boundary minimal surfaces of unbounded genus
• Free Boundary Minimal Surfaces in the Unit Three-Ball via Desingularization of the Critical Catenoid and the Equatorial Disk
• Equivariant min-max theory

Cited by in corpus (4)

• Free boundary minimal surfaces of any topological type in Euclidean balls via shape optimization
• Multiplicity one for min-max theory in compact manifolds with boundary and its applications
• Noncompact self-shrinkers for mean curvature flow with arbitrary genus
• Spectral estimates for free boundary minimal surfaces via Montiel-Ros partitioning methods