(Almgren’s big regularity theorem [5]) Let $L$ be a compactly supported $m$-dimensional closed integral current inside a complete Riemannian manifold, which minimizes the volume among all closed integral currents in the same homology class, then away from a closed subset $S\subset\text{supp}(L)$with Hausdorff dimension at most $m-2$, the rectifiable subset $\text{supp}(L)\setminus S$ is a smooth submanifold.