Stability properties for the higher dimensional catenoid in $\rr^{n+1}$

Abstract

This paper concerns some stability properties of higher dimensional catenoids in $\rr^{n+1}$ with $n\ge 3$. We prove that higher dimensional catenoids have index one. We use $\delta$-stablity for minimal hypersurfaces and show that the catenoid is $\frac{2}{n}$-stable and a complete $\frac{2}{n}$-stable minimal hypersurface is a catenoid or a hyperplane provided the second fundamental form satisfies some decay conditions.

15 pages

Cited by in corpus (1)

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