A Gap Theorem for Self-shrinkers of the Mean Curvature Flow in Arbitrary   Codimension
  In this paper, we prove a classification theorem for self-shrinkers of the mean curvature flow with $|A|^2\le 1$ in arbitrary codimension. In particular, this implies a gap theorem for self-shrinkers in arbitrary codimension. 
Huai-Dong Cao and Haizhong Li
math.DG