%0 Journal Article
%T Complete self-shrinkers of the mean curvature flow
%A Qing-Ming Cheng
%A Yejuan Peng
%J Mathematics
%D 2012
%I arXiv
%X It is our purpose to study complete self-shrinkers in Euclidean space. By introducing a generalized maximum principle for $\mathcal{L}$-operator, we give estimates on supremum and infimum of the squared norm of the second fundamental form of self-shrinkers without assumption on \emph{polynomial volume growth}, which is assumed in Cao and Li. Thus, we can obtain the rigidity theorems on complete self-shrinkers without assumption on \emph{polynomial volume growth}. For complete proper self-shrinkers of dimension 2 and 3, we give a classification of them under assumption of constant squared norm of the second fundamental form.
%U http://arxiv.org/abs/1202.1053v3