The superposition principle for local 1-dimensional currents

Fuente: arXiv
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Main Authors: Ambrosio, Luigi, Renzi, Federico, Vitillaro, Federico
Format: Preprint
Published: 2025
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author Ambrosio, Luigi
Renzi, Federico
Vitillaro, Federico
author_facet Ambrosio, Luigi
Renzi, Federico
Vitillaro, Federico
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2503_18157
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The superposition principle for local 1-dimensional currents
Ambrosio, Luigi
Renzi, Federico
Vitillaro, Federico
Metric Geometry
Analysis of PDEs
Functional Analysis
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.
title The superposition principle for local 1-dimensional currents
topic Metric Geometry
Analysis of PDEs
Functional Analysis
url https://arxiv.org/abs/2503.18157