Stability properties for the higher dimensional catenoid in ℝⁿ

By Luen-Fei Tam, Detang Zhou. 2007

52 citations recorded by the source corpus.

This paper concerns some stability properties of higher dimensional catenoids in R n+1 with n > 3. We prove that higher dimensional catenoids have index one. We use δ-stablity for minimal hypersurfaces and show that the catenoid is 2/n-stable and that a complete 2/n-stable minimal hypersurface is a catenoid or a hyperplane provided the second fundamental form satisfies some decay conditions.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c9eab58cff6f49dc7e0eda0c97c0f008f952015c