# Metric currents and polylipschitz forms

## TL;DR

This paper introduces a new space of polylipschitz forms on locally compact metric spaces, serving as a pre-dual to the space of metric currents, thus providing an analogue of differential forms in metric geometry.

## Contribution

It constructs a space of polylipschitz forms that acts as a pre-dual to metric currents, extending differential form concepts to metric spaces.

## Key findings

- Polylipschitz forms form a pre-dual to metric currents.
- Provides a differential form analogue in metric spaces.
- Establishes foundational tools for metric geometric analysis.

## Abstract

We construct, for a locally compact metric space $X$, a space of polylipschitz forms $\bar\Gamma^*_c(X)$, which is a pre-dual for the space of metric currents of $\mathscr{D}_*(X)$ Ambrosio and Kirchheim. These polylipschitz forms may be seen as a substitute of differential forms in the metric setting.