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.
Articolo in rivista - Articolo scientifico
Mathematics (all);
English
6-lug-2012
2013
141
3-4
363
390
reserved
Mongodi, S. (2013). Some applications of metric currents to complex analysis. MANUSCRIPTA MATHEMATICA, 141(3-4), 363-390 [10.1007/s00229-012-0575-9].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/349826
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