Curvature estimates for minimal submanifolds of higher codimension and   small G-rank
  We obtain new curvature estimates and Bernstein type results for minimal $n-$submanifolds in $\ir{n+m},\, m\ge 2$ under the condition that the rank of its Gauss map is at most 2. In particular, this applies to minimal surfaces in Euclidean spaces of arbitrary codimension. 
J. Jost, Y. L. Xin and Ling Yang
math.DG