Calculus of Variations and Geometric Measure Theory
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S. Mongodi

Some applications of metric currents to complex analysis

created by mongodi on 26 Jun 2013
modified by paolini on 19 Dec 2014


Published Paper

Inserted: 26 jun 2013
Last Updated: 19 dec 2014

Journal: Manuscripta Mathematica
Volume: 141
Number: 3-4
Pages: pp 363-390
Year: 2013
Doi: 10.1007/s00229-012-0575-9


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.

Tags: GeMeThNES


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