Minkowski content estimates for generic area minimizing hypersurfaces

2023/12/05 by Xuanyu Li, Li, Xuanyu · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2312.02950

openalex publication_date 2023/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Γ be a smooth, closed, oriented, (n-1)-dimensional submanifold of ℝⁿ⁺¹. It was shown by Chodosh-Mantoulidis-Schulze that one can perturb Γ to a nearby Γ' such that all minimizing currents with boundary Γ' 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 Γ' has Minkowski dimension less than n-9.

Cited by

• Minimal surfaces and comparison geometry

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