{
  "id": "1903.02654",
  "version": "v1",
  "published": "2019-03-06T23:23:45.000Z",
  "updated": "2019-03-06T23:23:45.000Z",
  "title": "Scattering resonances on truncated cones",
  "authors": [
    "Dean Baskin",
    "Mengxuan Yang"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "abstract": "We consider the problem of finding the resonances of the Laplacian on truncated Riemannian cones. In a similar fashion to Cheeger--Taylor, we construct the resolvent and scattering matrix for the Laplacian on cones and truncated cones. Following Stefanov, we show that the resonances on the truncated cone are distributed asymptotically as Ar^n + o(r^n), where A is an explicit coefficient. We also conclude that the Laplacian on a non-truncated cone has no resonances.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-06T23:23:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "33C10",
      "58J50"
    ],
    "keywords": [
      "scattering resonances",
      "truncated riemannian cones",
      "similar fashion",
      "explicit coefficient",
      "scattering matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}