Rectifiability of Flat Singular Points for Area-Minimizing mod 2Q Hypercurrents

Abstract

Abstract Consider an $ m $-dimensional area minimizing mod$ (2Q) $ current $ T $, with $ Q\in {\mathbb {N}} $, inside a sufficiently regular Riemannian manifold of dimension $ m + 1 $. We show that the set of singular density-$ Q $ points with a flat tangent cone is $ (m-2) $-rectifiable. This complements the thorough structural analysis of the singularities of area-minimizing hypersurfaces modulo $ p $ that has been completed in the series of works of De Lellis–Hirsch–Marchese–Stuvard and De Lellis–Hirsch–Marchese–Stuvard–Spolaor, and the work of Minter–Wickramasekera.