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. © 2012 Springer-Verlag.
Some applications of metric currents to complex analysis
MONGODI, SAMUELE
2013-01-01
Abstract
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. © 2012 Springer-Verlag.File in questo prodotto:
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