Calculus of Variations and Geometric Measure Theory

P. Bonicatto - G. Del Nin - E. Pasqualetto

Decomposition of integral metric currents

created by pasqualetto on 16 Apr 2021
modified by delnin on 12 Jan 2022


Published Paper

Inserted: 16 apr 2021
Last Updated: 12 jan 2022

Journal: J. Funct. Anal.
Volume: 282
Number: 7
Year: 2022

ArXiv: 2104.07593 PDF


In the setting of complete metric spaces, we prove that integral currents can be decomposed as a sum of indecomposable components. In the special case of one-dimensional integral currents, we also show that the indecomposable ones are exactly those associated with injective Lipschitz curves or injective Lipschitz loops, therefore extending Federer's characterisation to metric spaces. Moreover, some applications of our main results will be discussed.

Keywords: integral currents, metric currents, Indecomposable currents, Lipschitz curves