Weak KAM theory in higher-dimensional holonomic measure flows
Dynamical Systems
2025-07-08 v3 Analysis of PDEs
Optimization and Control
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.
Cite
@article{arxiv.1901.08181,
title = {Weak KAM theory in higher-dimensional holonomic measure flows},
author = {Rodolfo Rios-Zertuche},
journal= {arXiv preprint arXiv:1901.08181},
year = {2025}
}
Comments
29 pages. Full rewrite