{
  "id": "2305.03781",
  "version": "v1",
  "published": "2023-05-05T18:15:29.000Z",
  "updated": "2023-05-05T18:15:29.000Z",
  "title": "Rectifiability of flat singular points for area-minimizing mod$(2Q)$ hypercurrents",
  "authors": [
    "Anna Skorobogatova"
  ],
  "comment": "17 pages, 1 figure. arXiv admin note: text overlap with arXiv:2304.11555",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "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 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-05T18:15:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q15",
      "49Q05",
      "49N60",
      "35B65",
      "35J47"
    ],
    "keywords": [
      "flat singular points",
      "area-minimizing mod",
      "hypercurrents",
      "dimensional upper minkowski content",
      "rectifiability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}