A simple proof of the $1$-dimensional flat chain conjecture

TL;DR

This paper provides an elementary proof demonstrating that metric 1-currents in Euclidean space are equivalent to Federer-Fleming flat chains, simplifying the understanding of their relationship.

Contribution

It introduces a new, straightforward proof of the correspondence between metric 1-currents and flat chains, enhancing clarity and accessibility.

Findings

Establishes the equivalence between metric 1-currents and flat chains in Euclidean space.

Simplifies the proof of the 1-dimensional flat chain conjecture.

Provides an accessible approach to a fundamental result in geometric measure theory.

Abstract

We give a new, elementary proof of the fact that metric 1-currents in the Euclidean space correspond to Federer-Fleming flat chains.