  Combining the tools of geometric analysis with properties of Jordan angles
and angle space distributions, we derive a spherical and a Euclidean Bernstein
theorem for minimal submanifolds of arbitrary dimension and codimension, under
the condition that the Gauss image is contained in some geometrically defined
closed region of a Grassmannian manifold. The proof depends on the
subharmoncity of an auxiliary function, the Codazzi equations and geometric
measure theory.
