{
  "id": "2008.07329",
  "version": "v1",
  "published": "2020-08-17T14:02:21.000Z",
  "updated": "2020-08-17T14:02:21.000Z",
  "title": "Fixed angle inverse scattering in the presence of a Riemannian metric",
  "authors": [
    "Shiqi Ma",
    "Mikko Salo"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption on the metric, we obtain uniqueness and stability results in the inverse scattering problem for a potential with data generated by two incident waves from opposite directions. Further, similar results are given using one measurement provided the potential also satisfies a symmetry assumption. This work extends the results of [23,24] from the Euclidean case to certain Riemannian metrics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-17T14:02:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q60",
      "35J05",
      "31B10",
      "35R30",
      "78A40"
    ],
    "keywords": [
      "riemannian metric",
      "symmetry assumption",
      "fixed angle inverse scattering problem",
      "caustics condition",
      "similar results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}