{
  "id": "2303.08430",
  "version": "v1",
  "published": "2023-03-15T08:06:08.000Z",
  "updated": "2023-03-15T08:06:08.000Z",
  "title": "Reconstruction of a Lorentzian manifold from its Dirichlet-to-Neumann map",
  "authors": [
    "Alberto Enciso",
    "Michał Wrochna",
    "Gunther Uhlmann"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We prove that the Dirichlet-to-Neumann map of the linear wave equation determines the topological, differentiable and conformal structure of the underlying Lorentzian manifold, under mild technical assumptions. With more stringent geometric assumptions, the full Lorentzian structure of the manifold can be recovered as well. The key idea of the proof is to show that the singular support of the Schwartz kernel of the Dirichlet-to-Neumann map of a manifold completely determines the so-called boundary light observation set of the manifold together with its natural causal structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-15T08:06:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet-to-neumann map",
      "lorentzian manifold",
      "linear wave equation determines",
      "boundary light observation set",
      "reconstruction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}