{
  "id": "1609.09142",
  "version": "v1",
  "published": "2016-09-28T22:24:12.000Z",
  "updated": "2016-09-28T22:24:12.000Z",
  "title": "Minimal hypersurfaces and bordism of positive scalar curvature metrics",
  "authors": [
    "Boris Botvinnik",
    "Demetre Kazaras"
  ],
  "comment": "27 pages, 4 figures, comments welcome",
  "categories": [
    "math.DG",
    "math.AT",
    "math.GT"
  ],
  "abstract": "Let $(Y,g)$ be a compact Riemannian manifold of positive scalar curvature (psc). It is well-known, due to Schoen-Yau, that any closed stable minimal hypersurface of $Y$ also admits a psc-metric. We establish an analogous result for stable minimal hypersurfaces with free boundary. Furthermore, we combine this result with tools from geometric measure theory and conformal geometry to study psc-bordism. For instance, assume $(Y_0,g_0)$ and $(Y_1,g_1)$ are closed psc-manifolds equipped with stable minimal hypersurfaces $X_0 \\subset Y_0$ and $X_1\\subset Y_1$. Under natural topological conditions, we show that a psc-bordism $(Z,\\bar g) : (Y_0,g_0)\\rightsquigarrow (Y_1,g_1)$ gives rise to a psc-bordism between $X_0$ and $X_1$ equipped with the psc-metrics given by the Schoen-Yau construction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-28T22:24:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C27",
      "57R65",
      "58J05",
      "58J50"
    ],
    "keywords": [
      "positive scalar curvature metrics",
      "geometric measure theory",
      "psc-bordism",
      "compact riemannian manifold",
      "conformal geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}