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.
Mongodi, S. (2013). Some applications of metric currents to complex analysis. MANUSCRIPTA MATHEMATICA, 141(3-4), 363-390 [10.1007/s00229-012-0575-9].
Some applications of metric currents to complex analysis
MONGODI, SAMUELE
2013
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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