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arXiv · 2504.19234

Hausdorff measure bounds for density-$Q$ flat singularities of minimizing integral currents

Gianmarco Caldini·Anna Skorobogatova
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Abstract

In this article we prove that the set of flat singular points of locally highest density of area-minimizing integral currents of dimension $m$ and general codimension in a smooth Riemannian manifold $Σ$ has locally finite $(m-2)$-dimensional Hausdorff measure. In fact, the set of such flat singular points can be split into a union of two sets, one of which we show is locally $\mathcal{H}^{m-2}$-negligible, while for the other we obtain local $(m-2)$-dimensional Minkowski content bounds.

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Gianmarco Caldini, Anna Skorobogatova. 2025-04-27. Hausdorff measure bounds for density-$Q$ flat singularities of minimizing integral currents. https://arxiv.org/abs/2504.19234

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