Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-25T13:33:02.176Z Has data issue: false hasContentIssue false

Some fine properties of currents and applications to distributional Jacobians

Published online by Cambridge University Press:  12 July 2007

Camillo De Lellis
Scuola Normale Superiore P.zza dei Cavalieri 7, 56100 Pisa, Italy (


We study fine properties of currents in the framework of geometric measure theory on metric spaces developed by Ambrosio and Kirchheim, and we prove a rectifiability criterion for flat currents of finite mass. We apply these tools to study the structure of the distributional Jacobians of functions in the space BnV, defined by Jerrard and Soner. We define the subspace of special functions of bounded higher variation and we prove a closure theorem.

Research Article
Copyright © Royal Society of Edinburgh 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)