%0 Journal Article
%T A gap theorem of self-shrinkers
%A Qing-Ming Cheng
%A Guoxin Wei
%J Mathematics
%D 2012
%I arXiv
%X In this paper, we study complete self-shrinkers in Euclidean space and prove that an $n$-dimensional complete self-shrinker with polynomial volume growth in Euclidean space $\mathbb{R}^{n+1}$ is isometric to either $\mathbb{R}^{n}$, $S^{n}(\sqrt{n})$, or $\mathbb{R}^{n-m}\times S^m (\sqrt{m})$, $1\leq m\leq n-1$, if the squared norm $S$ of the second fundamental form is constant and satisfies $S<(10/7)$.
%U http://arxiv.org/abs/1212.6028v1