{
  "id": "1611.00462",
  "version": "v1",
  "published": "2016-11-02T03:44:03.000Z",
  "updated": "2016-11-02T03:44:03.000Z",
  "title": "Endpoint resolvent estimates for compact Riemannian manifolds",
  "authors": [
    "Rupert L. Frank",
    "Lukas Schimmer"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP",
    "math.CA",
    "math.SP"
  ],
  "abstract": "We prove $L^p\\to L^{p'}$ bounds for the resolvent of the Laplace-Beltrami operator on a compact Riemannian manifold of dimension $n$ in the endpoint case $p=2(n+1)/(n+3)$. It has the same behavior with respect to the spectral parameter $z$ as its Euclidean analogue, due to Kenig-Ruiz-Sogge, provided a parabolic neighborhood of the positive half-line is removed. This is region is optimal, for instance, in the case of a sphere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-02T03:44:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact riemannian manifold",
      "endpoint resolvent estimates",
      "spectral parameter",
      "parabolic neighborhood",
      "euclidean analogue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}