Area-minimizing hypersurfaces are generically smooth in ambient dimension 11 after a C-infinity-small perturbation of the boundary or metric, and in dimensions 12 and up the singular set has dimension at most n-10-epsilon_n.
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Generic regularity for minimizing hypersurfaces in dimension 11
Area-minimizing hypersurfaces are generically smooth in ambient dimension 11 after a C-infinity-small perturbation of the boundary or metric, and in dimensions 12 and up the singular set has dimension at most n-10-epsilon_n.