  Under suitable conditions on the range of the Gauss map of a complete
submanifold of Euclidean space with parallel mean curvature, we construct a
strongly subharmonic function and derive a-priori estimates for the harmonic
Gauss map. The required conditions here are more general than in previous work
and they therefore enable us to improve substantially previous results for the
Lawson-Osseman problem concerning the regularity of minimal submanifolds in
higher codimension and to derive Bernstein type results.
