2014/09/03 by Rodolfo Ríos-Zertuche, Rios-Zertuche, Rodolfo
Mathematics · #49Q15 (Primary) #53C65 #58A25 (Secondary) #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1409.1205
openalex publication_date 2014/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define holonomic measures to be certain analogues of varifolds that keep track of the local parameterization and orientation of the submanifold they represent. They are Borel measures on the direct sum of several copies of the tangent bundle. We show that there is an approximation to these by smooth singular chains whose boundaries and Lagrangian actions are controlled. As an illustration of the usefulness of this result, we show how this can be applied to study foliations on the torus. We give other applications elsewhere.