%0 Journal Article
%T On stable hypersurfaces with constant mean curvature in Euclidean spaces
%A Jinpeng Lu
%J Mathematics
%D 2012
%I arXiv
%X 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.
%U http://arxiv.org/abs/1212.3427v1