  In this paper, we obtain results on rigidity of complete Riemannian manifolds
with weighted Poincar\'e 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.
