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Some applications of metric currents to complex analysis. (English) Zbl 1267.32038
Summary: 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.

MSC:
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
46G20 Infinite-dimensional holomorphy
58B12 Questions of holomorphy and infinite-dimensional manifolds
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