Interior regularity of area minimizing currents within a $C^{2,α}$-submanifold
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916713265627136 |
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| author | Nardulli, Stefano Resende, Reinaldo |
| author_facet | Nardulli, Stefano Resende, Reinaldo |
| contents | Given an area-minimizing integral $m$-current in $Σ$, we prove that the Hausdorff dimension of the interior singular set of $T$ cannot exceed $m-2$, provided that $Σ$ is an embedded $(m+\bar{n})$-submanifold of $\mathbb{R}^{m+n}$ of class $C^{2,α}$, where $α>0$. This result establishes the complete counterpart, in the arbitrary codimension setting, of the interior regularity theory for area-minimizing integral hypercurrents within a Riemannian manifold of class $C^{2,α}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17407 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interior regularity of area minimizing currents within a $C^{2,α}$-submanifold Nardulli, Stefano Resende, Reinaldo Analysis of PDEs Differential Geometry 49Q15, 49Q05, 53A10, 49Q20 Given an area-minimizing integral $m$-current in $Σ$, we prove that the Hausdorff dimension of the interior singular set of $T$ cannot exceed $m-2$, provided that $Σ$ is an embedded $(m+\bar{n})$-submanifold of $\mathbb{R}^{m+n}$ of class $C^{2,α}$, where $α>0$. This result establishes the complete counterpart, in the arbitrary codimension setting, of the interior regularity theory for area-minimizing integral hypercurrents within a Riemannian manifold of class $C^{2,α}$. |
| title | Interior regularity of area minimizing currents within a $C^{2,α}$-submanifold |
| topic | Analysis of PDEs Differential Geometry 49Q15, 49Q05, 53A10, 49Q20 |
| url | https://arxiv.org/abs/2404.17407 |