Calculus of Variations and Geometric Measure Theory

E. Paolini - E. Stepanov

Decomposition of acyclic normal currents in a metric space

created by stepanov on 28 Jun 2011
modified by paolini on 12 Oct 2019


Published Paper

Inserted: 28 jun 2011
Last Updated: 12 oct 2019

Journal: J. Funct. Anal.
Volume: 263
Number: 11
Pages: 3358--3390
Year: 2012
Doi: 10.1016/j.jfa.2012.08.009

ArXiv: 1303.5664 PDF


We prove that every acyclic normal one-dimensional real Ambrosio-Kirchheim current in a Polish (i.e. complete separable metric) space can be decomposed in curves, thus generalizing the analogous classical result proven by S. Smirnov in Euclidean space setting. The same assertion is true for every complete metric space under a suitable set-theoretic assumption.

Keywords: currents, metric, decomposition