# Currents and Differential Forms in Metric Spaces

### (Rice University)

**Event:** ERC School on Analysis in Metric Spaces and Geometric Measure Theory

**Date:** Jan 13, 2011,
**time:** 15:50

**Place:** Centro De Giorgi, Scuola Normale Superiore

**Abstract.** In their 2000 paper, Ambrosio and Kirchheim generalize the currents

of Federer and Fleming to the setting of metric spaces. They replace the

notion of a differential form with an n-tuple of Lipschitz maps, and define a

metric current as a real-valued map on these n-tuples with certain properties.

I will discuss some properties of these metric currents, as well as explore the possibility of defining metric differential forms directly, so that metric currents may be defined as a proper dual space.