Generic regularity for minimizing hypersurfaces in dimension 11

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, $n+1\ge 12$, we prove in the same two contexts that area-minimizing hypersurfaces have at most an $n-10-\hat{I}{\mu }_n$ dimensional singular set after an arbitrarily $C^{\infty }$-small perturbation of the Plateau boundary or the ambient Riemannian metric, respectively.

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