{
  "id": "1605.06922",
  "version": "v1",
  "published": "2016-05-23T07:42:11.000Z",
  "updated": "2016-05-23T07:42:11.000Z",
  "title": "Quantitative C^1 - estimates on manifolds",
  "authors": [
    "Batu Güneysu",
    "Stefano Pigola"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We prove a $\\mathsf{C}^1$-elliptic estimate of the form $ \\sup_{B(x,r/2)} |\\mathrm{grad} (\\psi) | \\leq C \\left\\{ \\sup_{B(x,r)} |\\Delta \\psi| + \\sup_{B(x,r)} |\\psi| \\right\\}, $ valid on any complete Riemannian manifold $M$ and for any smooth function $\\psi$ which is defined in a nighbourhood of $B(x,r)$, with an explicit quantitative control on the constant $C=C(B(x,r))$ in terms of the curvature of the geodesic ball $B(x,r)\\subset M$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-23T07:42:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete riemannian manifold",
      "geodesic ball",
      "explicit quantitative control",
      "elliptic estimate",
      "smooth function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}