{
  "id": "2107.08354",
  "version": "v1",
  "published": "2021-07-18T03:38:03.000Z",
  "updated": "2021-07-18T03:38:03.000Z",
  "title": "$\\mathrm{K}$-cowaist on complete foliated manifolds",
  "authors": [
    "Guangxiang Su",
    "Xiangsheng Wang"
  ],
  "comment": "8 pages, comments are welcome!",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $(M,F)$ be a connected (not necessarily compact) foliated manifold carrying a complete Riemannian metric $g^{TM}$. We generalize Gromov's $\\mathrm{K}$-cowaist using the coverings of $M$, as well as defining a closely related concept called $\\widehat{\\mathrm{A}}$-cowaist. Let $k^F$ be the associated leafwise scalar curvature of $g^F = g^{TM}|_F$. We obtain some estimates on $k^F$ using these two concepts. In particular, assuming that the generalized $\\mathrm{K}$-cowaist is infinity and either $TM$ or $F$ is spin, we show that $\\inf(k^F)\\leq 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-18T03:38:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J20",
      "53C21",
      "53C12"
    ],
    "keywords": [
      "complete foliated manifolds",
      "complete riemannian metric",
      "associated leafwise scalar curvature",
      "generalize gromovs",
      "closely related concept"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}