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

We show that for an area minimizingm‐dimensional integral currentTof 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 approximateTalong blow‐up scales.

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John Wiley and Sons
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Communications on Pure and Applied Mathematics
Medium: X
Sponsoring Org:
National Science Foundation
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