Manifolds with weighted Poincaré inequality and uniqueness of minimal hypersurfaces

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dc.creatorCheng, Xu
dc.creatorZhou, Detang
dc.date2008-08-08
dc.date.accessioned2026-07-07T09:55:39Z
dc.date.available2026-07-07T09:55:39Z
dc.descriptionIn this paper, we obtain results on rigidity of complete Riemannian manifolds with weighted Poincaré inequality. As an application, we prove that if $M$ is a complete $\frac{n-2}{n}$-stable minimal hypersurface in $\mathbb{R}^{n+1}$ with $n\geq 3$ and has bounded norm of the second fundamental form, then $M$ must either have only one end or be a catenoid.
dc.identifierhttps://arxiv.org/abs/0808.1185
dc.identifierhttp://arxiv.org/abs/0808.1185
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/166706
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.subject58C42
dc.titleManifolds with weighted Poincaré inequality and uniqueness of minimal hypersurfaces
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