Weak KAM theory in higher-dimensional holonomic measure flows

2019/01/24 by Rodolfo Ríos-Zertuche, Rios-Zertuche, Rodolfo
Mathematics · Physics and Astronomy · #37J40 #37J50 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Optimization and Control (math.OC) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1901.08181

openalex publication_date 2019/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Normal and Integral Currents
• Action minimizing invariant measures for positive definite Lagrangian systems

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