The pointed flat compactness theorem for locally integral currents

TL;DR

This paper extends a recent compactness theorem for integral currents to locally integral currents in pointed metric spaces, introducing a new variant of Ambrosio--Kirchheim theory to handle currents with finite mass locally.

Contribution

It presents a generalized compactness theorem for locally integral currents in pointed metric spaces, expanding the scope of previous results and theory.

Findings

Established a new compactness theorem for locally integral currents

Introduced a variant of Ambrosio--Kirchheim theory for currents with finite local mass

Extended the applicability of integral current theory in metric spaces

Abstract

Recently, a new embedding/compactness theorem for integral currents in a sequence of metric spaces has been established by the second author. We present a version of this result for locally integral currents in a sequence of pointed metric spaces. To this end we introduce another variant of the Ambrosio--Kirchheim theory of currents in metric spaces, including currents with finite mass in bounded sets.