The Space-Time Connectivity Theorem for Normal 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_ | 1866914084179410944 |
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| author | Bonicatto, Paolo Rindler, Filip Turnbull, Harry |
| author_facet | Bonicatto, Paolo Rindler, Filip Turnbull, Harry |
| contents | This work establishes a Space-Time Connectivity Theorem for normal currents. In analogy to classical results by Federer and Fleming as well as a recent theorem for integral currents by the second author, this result allows one to witness the weak* convergence of a uniformly bounded sequence of boundaryless normal currents with a space-time normal current that connects the elements of the sequence with their limit. The space-time setting is distinguished from the classical case in that this connecting current has a time coordinate and thus constitutes a progressive-in-time way to deform an element of the sequence to the limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Space-Time Connectivity Theorem for Normal Currents Bonicatto, Paolo Rindler, Filip Turnbull, Harry Analysis of PDEs Functional Analysis 49Q15, 53C65 This work establishes a Space-Time Connectivity Theorem for normal currents. In analogy to classical results by Federer and Fleming as well as a recent theorem for integral currents by the second author, this result allows one to witness the weak* convergence of a uniformly bounded sequence of boundaryless normal currents with a space-time normal current that connects the elements of the sequence with their limit. The space-time setting is distinguished from the classical case in that this connecting current has a time coordinate and thus constitutes a progressive-in-time way to deform an element of the sequence to the limit. |
| title | The Space-Time Connectivity Theorem for Normal Currents |
| topic | Analysis of PDEs Functional Analysis 49Q15, 53C65 |
| url | https://arxiv.org/abs/2510.08360 |