Minkowski content estimates for generic area minimizing hypersurfaces

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 ${\Gamma }^{\prime }$ such that all minimizing currents with boundary ${\Gamma }^{\prime }$ 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 ${\Gamma }^{\prime }$ has Minkowski dimension less than $n-9$.

14 pages. Comments are welcome!

References in corpus (4)

• Generic regularity for minimizing hypersurfaces in dimensions 9 and 10
• Generic Regularity of Minimal Hypersurfaces in Dimension 8
• Improved generic regularity of codimension-1 minimizing integral currents
• Minimal hypersurfaces for generic metrics in dimension 8