Curvature Decay Estimates of Graphical Mean Curvature Flow in Higher   Codimensions
  We derive pointwise curvature estimates for graphical mean curvature flows in higher codimensions. To the best of our knowledge, this is the first such estimates without assuming smallness of first derivatives of the defining map. An immediate application is a convergence theorem of the mean curvature flow of the graph of an area decreasing map between flat Riemann surfaces. 
Knut Smoczyk, Mao-Pei Tsui and Mu-Tao Wang
math.DG