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Some applications of metric currents to complex analysis

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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.

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  1. Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy

    Samuele Mongodi

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  1. Samuele Mongodi
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Mongodi, S. Some applications of metric currents to complex analysis. manuscripta math. 141, 363–390 (2013). https://doi.org/10.1007/s00229-012-0575-9

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  • DOI: https://doi.org/10.1007/s00229-012-0575-9

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