Calculus of Variations and Geometric Measure Theory

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