Currents and Differential Forms in Metric Spaces


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.

Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy