Index of the critical catenoid

2016/09/08 by Baptiste Devyver, Devyver, Baptiste · 5 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1609.02315

openalex publication_date 2016/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we show that the critical catenoid, as a free boundary minimal surface of the unit ball in ℝ³, has index 4. We also prove that a free boundary minimal surface of the unit ball in ℝ³, that is not a flat disk, has index at least 4.

Citations

• Embedded minimal tori in S3 and the Lawson conjecture
• Index estimates for free boundary minimal hypersurfaces
• The Morse index of the critical catenoid

Cited by

• A degenerate free boundary minimal annulus and non-uniqueness in spherical caps beyond the hemisphere
• Free boundary and capillary minimal surfaces in spherical caps II: Low energy
• The Y-Cone type Free Boundary Minimal Surfaces in the unit ball
• Boundary Curves of Free Boundary Minimal Surfaces
• Minmax Hierarchies and Minimal Surfaces in Manifolds

Related

• The Morse index of the critical catenoid
• Characterization of embedded free boundary surfaces in the ball
• A free boundary minimal surface via a 6-sweepout
• Genus one critical catenoid
• A Characterization of the Critical Catenoid