English

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

Analysis of PDEs 2023-06-19 v2 Differential Geometry

Abstract

Consider an mm-dimensional area minimizing mod(2Q)(2Q) current TT, with QNQ\in\mathbb{N}, inside a sufficiently regular Riemannian manifold of dimension m+1m + 1. We show that the set of singular density-QQ points with a flat tangent cone is countably (m2)(m-2)-rectifiable and has locally finite (m2)(m-2)-dimensional upper Minkowski content. This complements the thorough structural analysis of the singularities of area-minimizing hypersurfaces modulo pp 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.

Keywords

Cite

@article{arxiv.2305.03781,
  title  = {Rectifiability of flat singular points for area-minimizing mod$(2Q)$ hypercurrents},
  author = {Anna Skorobogatova},
  journal= {arXiv preprint arXiv:2305.03781},
  year   = {2023}
}

Comments

17 pages, 1 figure. arXiv admin note: text overlap with arXiv:2304.11555

R2 v1 2026-06-28T10:27:18.410Z