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arXiv · 2603.03100

Area minimising hypersurfaces mod $p$ do not admit immersed branch points

Paul Minter·Sidney Stanbury
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Abstract

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.

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Paul Minter, Sidney Stanbury. 2026-03-03. Area minimising hypersurfaces mod $p$ do not admit immersed branch points. https://arxiv.org/abs/2603.03100

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