{
  "id": "2206.06554",
  "version": "v1",
  "published": "2022-06-14T02:11:32.000Z",
  "updated": "2022-06-14T02:11:32.000Z",
  "title": "Minkowski inequality in Cartan-Hadamard manifolds",
  "authors": [
    "Mohammad Ghomi",
    "Joel Spruck"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DG",
    "math.AP",
    "math.MG"
  ],
  "abstract": "Using harmonic mean curvature flow, we establish a sharp Minkowski type lower bound for total mean curvature of convex surfaces with a given area in Cartan-Hadamard 3-manifolds. This inequality also improves the known estimates for total mean curvature in hyperbolic 3-space. As an application, we obtain a Bonnesen-style isoperimetric inequality for surfaces with convex distance function in nonpositively curved 3-spaces, via monotonicity results for total mean curvature. This connection between the Minkowski and isoperimetric inequalities is extended to Cartan-Hadamard manifolds of any dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-14T02:11:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "58J05",
      "52A38",
      "49Q15"
    ],
    "keywords": [
      "cartan-hadamard manifolds",
      "total mean curvature",
      "minkowski inequality",
      "sharp minkowski type lower bound",
      "isoperimetric inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}