{
  "id": "1202.0333",
  "version": "v2",
  "published": "2012-02-02T00:39:35.000Z",
  "updated": "2013-11-15T13:09:13.000Z",
  "title": "On Open Scattering Channels for Manifolds with Ends",
  "authors": [
    "Rainer Hempel",
    "Olaf Post",
    "Ricardo Weder"
  ],
  "comment": "updated version, now 43 pages",
  "journal": "Journal of Functional Analysis, 266, (5526--5583) 2014",
  "doi": "10.1016/j.jfa.2014.01.025",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "In the framework of time-dependent geometric scattering theory, we study the existence and completeness of the wave operators for perturbations of the Riemannian metric for the Laplacian on a complete manifold of dimension $n$. The smallness condition for the perturbation is expressed (intrinsically and coordinate free) in purely geometric terms using the harmonic radius; therefore, the size of the perturbation can be controlled in terms of local bounds on the injectivity radius and the Ricci-curvature. As an application of these ideas we obtain a stability result for the scattering matrix with respect to perturbations of the Riemannian metric. This stability result implies that a scattering channel which interacts with other channels preserves this property under small perturbations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-15T13:09:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J50",
      "34P25",
      "37A40",
      "81U99"
    ],
    "keywords": [
      "open scattering channels",
      "riemannian metric",
      "stability result implies",
      "time-dependent geometric scattering theory",
      "channels preserves"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.0333H"
    }
  }
}