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

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dc.creatorTam, Luen-Fei
dc.creatorZhou, Detang
dc.date2007-08-24
dc.date.accessioned2026-07-07T08:25:24Z
dc.date.available2026-07-07T08:25:24Z
dc.descriptionThis 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 $δ$-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.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/0708.3310
dc.identifierhttp://arxiv.org/abs/0708.3310
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136642
dc.subjectDifferential Geometry
dc.subject53A10; 53C42
dc.titleStability properties for the higher dimensional catenoid in $\rr^{n+1}$
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