Preprint

Inserted: 5 sep 2024
Last Updated: 5 sep 2024

Year: 2024

Abstract:

We prove that the singular set of an $m$-dimensional integral current $T$ in $\mathbb{R}^{n + m}$, semicalibrated by a $C^{2, \kappa_0}$ $m$-form $\omega$ 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 \cite{DLSk1, DLSk2, DMS} for area-minimizing currents to this setting.

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