  In this paper, we derive curvature estimates for strongly stable
hypersurfaces with constant mean curvature immersed in $\mathbb{R}^{n+1}$,
which show that the locally controlled volume growth yields a globally
controlled volume growth if $\partial M=\emptyset$. Moreover, we deduce a
Bernstein-type theorem for complete stable hypersurfaces with constant mean
curvature of arbitrary dimension, given a finite $L^p$-norm curvature
condition.
