Lipschitz Chain Approximation of Metric Integral Currents

TL;DR

This paper demonstrates that in locally compact metric spaces, integral currents can be approximated by Lipschitz chains with controlled mass, assuming slight extensions of Lipschitz maps are possible.

Contribution

It introduces a Lipschitz chain approximation method for integral currents in metric spaces under mild extension conditions.

Findings

Approximation of integral currents by Lipschitz chains with bounded mass

Extension property of Lipschitz maps facilitates approximation

Applicable to locally compact metric spaces

Abstract

Every integral current in a locally compact metric space $X$ can be approximated by a Lipschitz chain with respect to the normal mass, provided that Lipschitz maps into $X$ can be extended slightly.