Communications in Analysis and Geometry

Volume 19 (2011)

Number 1

The pointed flat compactness theorem for locally integral currents

Pages: 159 – 189



Urs Lang (Department of Mathematics, ETH Zurich, Switzerland)

Stefan Wenger (Department of Mathematics, University of Illinois at Chicago)


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.

Full Text (PDF format)