The Bernstein Problem in the Heisenberg Group
  We establish the following theorem of Bernstein type for the first Heisenberg group: Let S be a C^2 connected H-minimal surface which is a graph over some plane P, then S is either a non-characteristic vertical plane, or its generalized seed curve satisfies a type of constant curvature condition. 
Nicola Garofalo and Scott D. Pauls