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An upper Minkowski dimension estimate for the interior singular set of area minimizing currents
Communications on Pure and Applied Mathematics ( IF 3.1 ) Pub Date : 2023-09-18 , DOI: 10.1002/cpa.22165 Anna Skorobogatova 1
Communications on Pure and Applied Mathematics ( IF 3.1 ) Pub Date : 2023-09-18 , DOI: 10.1002/cpa.22165 Anna Skorobogatova 1
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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 . This provides a strengthening of the existing -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:
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。这加强了现有的由 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。
更新日期:2023-09-18
中文翻译:
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。这加强了现有的由 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。