  Let S be a C^2 H-minimal noncharacteristic hypersurface in the first
Heisenberg group. We show that if S contains a graphical strip, then it is not
a stable minimal surface. Moreover, we show that if S is a C^2 H-minimal
noncharacteristic entire graph which is not itself a vertical plane, then S
contains a graphical strip. Thus, as a corollary, we obtain an analogue of the
Bernstein theorem: the only stable C^2 H-minimal noncharacteristic entire
graphs are the vertical planes.
