Published Paper

Inserted: 25 mar 2025
Last Updated: 6 oct 2025

Journal: Nonlinear Analysis
Volume: 262
Year: 2026

Abstract:

We prove that every one-dimensional locally normal metric current, intended in the sense of U. Lang and S. Wenger, admits a nice integral representation through currents associated to (possibly unbounded) curves with locally finite length, generalizing the result shown by E. Paolini and E. Stepanov in the special case of Ambrosio-Kirchheim normal currents. Our result holds in Polish spaces, or more generally in complete metric spaces for 1-currents with tight support.