{
  "id": "2307.03616",
  "version": "v1",
  "published": "2023-07-07T14:13:37.000Z",
  "updated": "2023-07-07T14:13:37.000Z",
  "title": "A Poincaré formula for differential forms and applications",
  "authors": [
    "Nicolas Ginoux",
    "Georges Habib",
    "Simon Raulot"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We prove a new general Poincar\\'e-type inequality for differential forms on compact Riemannian manifolds with nonempty boundary. When the boundary is isometrically immersed in Euclidean space, we derive a new inequality involving mean and scalar curvatures of the boundary only and characterize its limiting case in codimension one. A new Ros-type inequality for differential forms is also derived assuming the existence of a nonzero parallel form on the manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-07T14:13:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "53C24",
      "58J32",
      "58J50"
    ],
    "keywords": [
      "differential forms",
      "applications",
      "general poincare-type inequality",
      "nonzero parallel form",
      "compact riemannian manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}