Rectifiability of flat singular points for area-minimizing mod(2Q) hypercurrents

2023/05/05 by Anna Skorobogatova, Skorobogatova, Anna · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Analytic and geometric function theory #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2305.03781

Abstract

Consider an m-dimensional area minimizing mod(2Q) current T, with Q∈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 countably (m-2)-rectifiable and has locally finite (m-2)-dimensional upper Minkowski content. 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.

Cited by

• Structure of two-dimensional mod(q) area-minimizing currents near flat singularities: the codimension one case

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