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arXiv · 2312.02950

Minkowski content estimates for generic area minimizing hypersurfaces

Xuanyu Li
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Abstract

Let $\Gamma$ be a smooth, closed, oriented, $(n-1)$-dimensional submanifold of $\mathbb{R}^{n+1}$. It was shown by Chodosh-Mantoulidis-Schulze that one can perturb $\Gamma$ to a nearby $\Gamma'$ such that all minimizing currents with boundary $\Gamma'$ are smooth away from a set with Hausdorff dimension less than $n-9$. We prove that the perturbation can be made such that the singular set of the minimizing current with boundary $\Gamma'$ has Minkowski dimension less than $n-9$.

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Xuanyu Li. 2023-12-05. Minkowski content estimates for generic area minimizing hypersurfaces. https://doi.org/10.1007/s00526-024-02791-9

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