  This short note is the announcement of a forthcoming work in which we prove a
first general boundary regularity result for area-minimizing currents in higher
codimension, without any geometric assumption on the boundary, except that it
is an embedded submanifold of a Riemannian manifold, with a mild amount of
smoothness ($C^{3, a_0}$ for a positive $a_0$ suffices). Our theorem allows to
answer a question posed by Almgren at the end of his Big Regularity Paper. In
this note we discuss the ideas of the proof and we also announce a theorem
which shows that the boundary regularity is in general weaker that the interior
regularity. Moreover we remark an interesting elementary byproduct on boundary
monotonicity formulae.
