  Moser's Bernstein theorem \cite{moser61} says that an entire minimal graph of
codimension 1 with bounded slope must be a hyperplane. An analogous result for
arbitrary codimension is not true, by an example of Lawson-Osserman. Here, we
show that Moser's theorem nevertheless extends to codimension 2, i.e., a
minimal $p$-submanifold in $R^{p+2}$, which is the graph of a smooth function
defined on the entire $R^p$ with bounded slope, must be a $p$-plane. Our method
depends on convexity properties of Grassmannians which come into play as the
targets of the (harmonic) Gauss maps of our minimal submanifolds. In fact, we
develop a general method to construct subsets of complete Riemannian manifolds
that cannot contain images of non-constant harmonic maps from compact
manifolds. When applied to Grassmannians, for codimension 2, it yields an
appropriate domain that cannot contain nontrivial images of such harmonic maps.
Our conclusion will then be reached by an application of Allard's theorem to
handle the issue that the minimal submanifolds in question are not compact.
