# Currents and Differential Forms in Metric Spaces

### 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.

Date
Location
Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy