Free boundary minimal annuli in $S^2_+\times S^1$
Abstract
Abstract Let M be a compact three-dimensional Riemannian manifold with non-negative Ricci curvature and a non-empty boundary $\partial M$ . Fraser and Li [2] established a compactness theorem for the space of compact, properly embedded minimal surfaces of fixed topological type in M with a free boundary on $\partial M$ , assuming that $\partial M$ is strictly convex with respect to the inward unit normal. In this paper, we show that the strict convexity condition on $\partial M$ cannot be relaxed.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Advanced Operator Algebra Research
Publication details
- Journal / source
- Proceedings of the Edinburgh Mathematical Society
- Publisher
- Cambridge University Press (CUP)
- Pages
- 1–4
- Publication date
- 13 April 2026
- Language
- EN