Mathematics > Metric Geometry
[Submitted on 23 Mar 2025
]
Title: The superposition principle for local 1-dimensional currents
Title: 局部一维电流的叠加原理
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.
Submission history
From: Federico Vitillaro [view email][v1] Sun, 23 Mar 2025 17:55:44 UTC (207 KB)
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