An upper Minkowski dimension estimate for the interior singular set of area minimizing currents

Abstract We show that for an area minimizing m ‐dimensional integral current T of codimension at least two inside a sufficiently regular Riemannian manifold, the upper Minkowski dimension interior singular set is most . This provides strengthening existing Hausdorff bound due to Almgren and De Lellis & Spadaro. As by‐product proof, we establish improvement on persistence singularities along sequence center manifolds taken approximate blow‐up scales.