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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.03037 |
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| _version_ | 1866909328323117056 |
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| author | Minter, Paul Parise, Davide Skorobogatova, Anna Spolaor, Luca |
| author_facet | Minter, Paul Parise, Davide Skorobogatova, Anna Spolaor, Luca |
| contents | We prove that the singular set of an $m$-dimensional integral current $T$ in $\mathbb{R}^{n + m}$, semicalibrated by a $C^{2, κ_0}$ $m$-form $ω$ is countably $(m - 2)$-rectifiable. Furthermore, we show that there is a unique tangent cone at $\mathcal{H}^{m - 2}$-a.e. point in the interior singular set of $T$. Our proof adapts techniques that were recently developed in [DLS23a, DLS23b, DLMS23] for area-minimizing currents to this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03037 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents Minter, Paul Parise, Davide Skorobogatova, Anna Spolaor, Luca Analysis of PDEs We prove that the singular set of an $m$-dimensional integral current $T$ in $\mathbb{R}^{n + m}$, semicalibrated by a $C^{2, κ_0}$ $m$-form $ω$ is countably $(m - 2)$-rectifiable. Furthermore, we show that there is a unique tangent cone at $\mathcal{H}^{m - 2}$-a.e. point in the interior singular set of $T$. Our proof adapts techniques that were recently developed in [DLS23a, DLS23b, DLMS23] for area-minimizing currents to this setting. |
| title | Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.03037 |