Inserted: 6 feb 2019
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.