Near a multiplicity-two plane, a stationary integral varifold with a topological separation condition in flat low-density cylinders is a generalized C^{1,alpha} two-valued graph with unique tangent cones.
Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents
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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 [DLS23a, DLS23b, DLMS23] for area-minimizing currents to this setting.
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On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes
Near a multiplicity-two plane, a stationary integral varifold with a topological separation condition in flat low-density cylinders is a generalized C^{1,alpha} two-valued graph with unique tangent cones.