{
  "id": "1807.03680",
  "version": "v1",
  "published": "2018-07-10T14:40:14.000Z",
  "updated": "2018-07-10T14:40:14.000Z",
  "title": "On the s-injectivity of the X-ray transform on manifolds with hyperbolic trapped set",
  "authors": [
    "Thibault Lefeuvre"
  ],
  "comment": "24 pages, 2 figures",
  "categories": [
    "math.AP",
    "math.DG",
    "math.DS"
  ],
  "abstract": "For smooth compact connected manifolds with strictly convex boundary, no conjugate points and a hyperbolic trapped set, we prove an equivalence principle concerning the injectivity of the X-ray transform $I_m$ on symmetric solenoidal tensors and the surjectivity of on a operator ${\\pi_m}_*$ on the set of solenoidal tensors. This allows us to establish the injectivity of the X-ray transform on solenoidal tensors of any order in the case of a surface satisfying these assumptions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-10T14:40:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D20",
      "37D40",
      "35R30"
    ],
    "keywords": [
      "hyperbolic trapped set",
      "x-ray transform",
      "s-injectivity",
      "symmetric solenoidal tensors",
      "smooth compact connected manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}