Generic regularity for minimizing hypersurfaces in dimension 11

2025/06/15 by Chodosh, Otis, Mantoulidis, Christos, Schulze, Felix +1 · 1 citation
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.12852

Abstract

We prove that area-minimizing hypersurfaces are generically smooth in ambient dimension 11 in the context of the Plateau problem and of area minimization in integral homology. For higher ambient dimensions, n+1 ≥ 12, we prove in the same two contexts that area-minimizing hypersurfaces have at most an n-10-ε_n dimensional singular set after an arbitrarily C^∞-small perturbation of the Plateau boundary or the ambient Riemannian metric, respectively.

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• Linearized equation and generic regularity in the Alt-Caffarelli problem

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