Weak KAM theory for subriemannian Lagrangians

TL;DR

This paper extends weak KAM theory to sub-Riemannian manifolds, providing a framework for analyzing Lagrangian dynamics constrained to horizontal distributions.

Contribution

It introduces a novel extension of weak KAM theory to sub-Riemannian settings using Tonelli's theorem for Lagrangian dynamics.

Findings

Established weak KAM solutions in sub-Riemannian contexts

Connected sub-Riemannian geometry with variational principles

Provided new tools for analyzing constrained dynamical systems

Abstract

We extend weak KAM theory to Lagrangians that are defined only on the horizontal distribution of a sub-Riemannian manifold. The main tool is Tonelli's theorem which allows dispending on a Lagrangian dynamics.