Inserted: 26 jun 2013
Last Updated: 19 dec 2014
Journal: Manuscripta Mathematica
Pages: pp 363-390
The aim of this paper is to extend the theory of metric currents, developed by Ambrosio and Kirchheim, to complex spaces. We define the bidimension of a metric current on a complex space and we discuss the Cauchy–Riemann equation on a particular class of singular spaces. As another application, we investigate the Cauchy–Riemann equation on complex Banach spaces, by means of a homotopy formula.