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

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

2007-08-24

arxiv.org/abs/0708.3310v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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 $\frac 2n$-stable and a complete $\frac 2n$-stable minimal hypersurface is a catenoid or a hyperplane provided the second fundamental form satisfies some decay conditions.

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