Area minimising hypersurfaces mod $p$ do not admit immersed branch points
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913025725825024 |
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| author | Minter, Paul Stanbury, Sidney |
| author_facet | Minter, Paul Stanbury, Sidney |
| contents | We show that area minimising hypersurfaces mod $p$ do not admit immersed branch points, namely branch points about which all classical singularities are immersed. Furthermore, we show that if an $n$-dimensional area minimising hypersurface mod $p$ is smoothly immersed outside a $\mathcal{H}^{n-1}$-null set, then it is in fact smoothly immersed outside a closed set of Hausdorff dimension at most $n-3$.
These results are consequences of a more general analysis of immersed stable minimal hypersurfaces with a certain `alternating' orientation. Indeed, our proof does not rely on the minimising property other than through stationarity, stability, and the verification of simple structural properties of the hypersurface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03100 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Area minimising hypersurfaces mod $p$ do not admit immersed branch points Minter, Paul Stanbury, Sidney Differential Geometry Analysis of PDEs 53A10, 49Q20, 35J60 We show that area minimising hypersurfaces mod $p$ do not admit immersed branch points, namely branch points about which all classical singularities are immersed. Furthermore, we show that if an $n$-dimensional area minimising hypersurface mod $p$ is smoothly immersed outside a $\mathcal{H}^{n-1}$-null set, then it is in fact smoothly immersed outside a closed set of Hausdorff dimension at most $n-3$. These results are consequences of a more general analysis of immersed stable minimal hypersurfaces with a certain `alternating' orientation. Indeed, our proof does not rely on the minimising property other than through stationarity, stability, and the verification of simple structural properties of the hypersurface. |
| title | Area minimising hypersurfaces mod $p$ do not admit immersed branch points |
| topic | Differential Geometry Analysis of PDEs 53A10, 49Q20, 35J60 |
| url | https://arxiv.org/abs/2603.03100 |