{
  "id": "1712.04545",
  "version": "v1",
  "published": "2017-12-12T21:49:12.000Z",
  "updated": "2017-12-12T21:49:12.000Z",
  "title": "Macroscopic stability and simplicial norms of hypersurfaces",
  "authors": [
    "Hannah Alpert"
  ],
  "comment": "9 pages",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "We introduce a $\\mathbb{Z}$--coefficient version of Guth's macroscopic stability inequality for almost-minimizing hypersurfaces. In manifolds with a lower bound on macroscopic scalar curvature, we use the inequality to prove a lower bound on areas of hypersurfaces in terms of the Gromov simplicial norm of their homology classes. We give examples to show that a very positive lower bound on macroscopic scalar curvature does not necessarily imply an upper bound on the areas of minimizing hypersurfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-12T21:49:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C23",
      "53A10"
    ],
    "keywords": [
      "hypersurfaces",
      "macroscopic scalar curvature",
      "lower bound",
      "guths macroscopic stability inequality",
      "gromov simplicial norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}