  We construct a weak KAM theory for higher-dimensional holonomic measures. We
define their slices and curves of those slices. We find a weak KAM solution in
that context, and we show that in many cases it corresponds to an exact form
that satisfies a version of the Hamilton-Jacobi equation. Along the way, we
give a characterization of minimizable Lagrangians, as well as some abstract
weak KAM machinery.
