Homogenization on arbitrary manifolds

TL;DR

This paper develops a general framework for homogenizing convex Hamiltonians on abelian covers of any compact manifold, offering a straightforward variational proof of existing homogenization results.

Contribution

It introduces a universal setting for homogenization on arbitrary manifolds and simplifies proofs of classical results using variational methods.

Findings

Established a homogenization framework on arbitrary manifolds.

Provided a simple variational proof for standard homogenization results.

Extended homogenization theory beyond traditional settings.

Abstract

We describe a setting for homogenization of convex hamiltonians on abelian covers of any compact manifold. In this context we also provide a simple variational proof of standard homogenization results.