October 15, 2025Open Access

Generic regularity for minimizing hypersurfaces in dimension 11

OCOtis ChodoshStanford University CMChristos MantoulidisRice University FSFelix SchulzeUniversity of Warwick

Key Points

Area-minimizing hypersurfaces are generically smooth in dimension 11, showing broad regularity.
For dimensions 12 and higher, hypersurfaces exhibit limited singular sets under small perturbations.
The study addresses the Plateau problem and integral homology in relation to these geometrical objects.
The findings contribute to understanding the nature of singular sets in higher-dimensional geometric contexts.

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-εₙ dimensional singular set after an arbitrarily C^-small perturbation of the Plateau boundary or the ambient Riemannian metric, respectively.

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