Free Boundary Minimal surfaces in the Euclidean Three-Ball close to the boundary
Abstract
abstract: We construct free boundary minimal surfaces (FBMS) embedded in the unit ball in the Euclidean three-space which are compact, lie arbitrarily close to the boundary unit sphere, are of genus zero, and their boundary has an arbitrarily large number of connected boundary components. The construction is by PDE gluing methods and the surfaces are desingularizations of unions of many catenoidal annuli and two flat discs. The union of the boundaries of the catenoidal annuli and discs is the union of a large finite number of parallel circles contained in the unit sphere, with each parallel circle contained in the boundary of exactly two of the catenoidal annuli and discs.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- American Journal of Mathematics
- Publisher
- Project MUSE
- Volume
- 148
- Issue
- 3
- Pages
- 681–729
- Publication date
- 30 May 2026
- Language
- EN