Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents

Abstract

We prove that the singular set of an $m$-dimensional integral current $T$ in ${\mathbb{R}}^{n+m}$, semicalibrated by a $C^{2,\hat{I}{º}_0}$ $m$-form $\ddot{I}‰$ 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 [DLS23a, DLS23b, DLMS23] for area-minimizing currents to this setting.

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