The superposition principle for local 1-dimensional currents
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909549758251008 |
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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 |