  It is well-known that a minimal graph of codimension one is stable, i.e. the
second variation of the area functional is non-negative. This is no longer true
for higher codimensional minimal graphs. In this note, we prove that a minimal
graph of any codimension is stable if its normal bundle is flat. We also prove
minimal graphs of dimension no greater than six and any codimension is flat if
the the normal bundle is flat and the density at infinity is finite. Such a
Bernstein type theorem holds in any dimension if we assume additionally growth
conditions on the volume element.
