{
  "id": "2305.06916",
  "version": "v1",
  "published": "2023-05-11T16:00:30.000Z",
  "updated": "2023-05-11T16:00:30.000Z",
  "title": "Unique continuation estimates on manifolds with Ricci curvature bounded below",
  "authors": [
    "Christian Rose",
    "Martin Tautenhahn"
  ],
  "comment": "23 pages, comments welcome!",
  "categories": [
    "math.AP",
    "math-ph",
    "math.DG",
    "math.FA",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We prove quantitative unique continuation estimates for relatively dense sets and spectral subspaces associated to small energies of Schr\\\"odinger operators on Riemannian manifolds with Ricci curvature bounded below. The upper bound for the energy range and the constant appearing in the estimate are given in terms of the lower bound of the Ricci curvature and the parameters of the relatively dense set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-11T16:00:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ricci curvature",
      "relatively dense set",
      "quantitative unique continuation estimates",
      "spectral subspaces",
      "lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}