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 of the interior singular set is at most $m-2$. This provides a strengthening of the existing $(m-2)$-dimensional Hausdorff dimension bound due to Almgren and De Lellis & Spadaro. As a by-product of the proof, we establish an improvement on the persistence of singularities along the sequence of center manifolds taken to approximate T along blow-up scales.

中文翻译：

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面积最小化电流的内部奇异集的上闵可夫斯基维数估计

我们证明，对于在足够规则的黎曼流形内至少有两个余维的m维积分流T最小化的区域，内部奇异集的上明可夫斯基维最多为$米-2$。这加强了现有的$（米-2）$由 Almgren 和 De Lellis & Spadaro 提出的 - 维 Hausdorff 维数界限。作为证明的副产品，我们对沿中心流形序列的奇点持久性进行了改进，以沿爆炸尺度近似T。