Classification and rigidity of self-shrinkers in the Mean curvature flow
  In this paper, we first use the method of Colding and Minicozzi [5] to show that K. Smoczyk's classification theorem [16] for complete self-shrinkers in higher codimension also holds under a weaker condition. Then as an application, we give some rigidity results for self-shrinkers in arbitrary codimension. 
Haizhong Li and Yong Wei
math.DG