{
  "id": "2103.09737",
  "version": "v1",
  "published": "2021-03-17T15:48:45.000Z",
  "updated": "2021-03-17T15:48:45.000Z",
  "title": "Scalar curvature, mean curvature and harmonic maps to the circle",
  "authors": [
    "Xiaoxiang Chai",
    "Inkang Kim"
  ],
  "comment": "13 pages, 1 figure; comments welcome",
  "categories": [
    "math.DG",
    "gr-qc",
    "math.AP",
    "math.GT"
  ],
  "abstract": "We study harmonic maps from a 3-manifold with boundary to $\\mathbb{S}^1$ and prove a special case of dihedral rigidity of three dimensional cubes whose dihedral angles are $\\pi / 2$. Furthermore we give some applications to mapping torus hyperbolic 3-manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-17T15:48:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C43",
      "53C21",
      "53C25"
    ],
    "keywords": [
      "mean curvature",
      "scalar curvature",
      "study harmonic maps",
      "special case",
      "dihedral rigidity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}