Weak KAM theory in higher-dimensional holonomic measure flows

Abstract

We construct a weak KAM theory for parameterized cobordisms and their relaxation, holonomic measures. 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.

29 pages. Full rewrite

References in corpus (2)

• Weak KAM theorem on non compact manifolds
• Characterization of minimizable Lagrangian action functionals and a dual Mather theorem