2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166706In 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.Differential GeometryGeometric Topology58C42text