Currents and Differential Forms in Metric Spaces

Colin Carroll

(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.