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Peer-reviewedCC BY-NC-NDCommunications of the American Mathematical Society

Rigidity in the Lorentzian Calderón problem with formally determined data

  • Lauri Oksanen
  • Rakesh
  • Mikko Salo
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Abstract

We study the Lorentzian Calderón problem, where the objective is to determine a globally hyperbolic Lorentzian metric up to a boundary fixing diffeomorphism from boundary measurements given by the hyperbolic Dirichlet-to-Neumann map. This problem is a wave equation analogue of the Calderón problem on Riemannian manifolds. We prove that if a globally hyperbolic metric agrees with the Minkowski metric outside a compact set and has the same hyperbolic Dirichlet-to-Neumann map as the Minkowski metric, then it must be the Minkowski metric up to diffeomorphism. In fact this follows from a stronger result that solves a formally determined inverse problem with a much smaller amount of measurements. To prove these results we introduce a new method for geometric hyperbolic inverse problems. The method is based on distorted plane wave solutions and on a combination of geometric, topological and unique continuation arguments.

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Cite

BibTeXRIS
BibTeX
@article{oksanen2026rigidity,
  title = {{Rigidity in the Lorentzian Calderón problem with formally determined data}},
  author = {Lauri Oksanen and Rakesh and Mikko Salo},
  journal = {Communications of the American Mathematical Society},
  year = {2026},
  month = jun,
  doi = {10.1090/cams/73},
  url = {https://doi.org/10.1090/cams/73},
  note = {CC BY-NC-ND},
}
RIS
TY  - JOUR
TI  - Rigidity in the Lorentzian Calderón problem with formally determined data
AU  - Lauri Oksanen
AU  - Rakesh
AU  - Mikko Salo
PY  - 2026
DA  - 2026/06/29
JO  - Communications of the American Mathematical Society
DO  - 10.1090/cams/73
UR  - https://doi.org/10.1090/cams/73
AB  - We study the Lorentzian Calderón problem, where the objective is to determine a globally hyperbolic Lorentzian metric up to a boundary fixing diffeomorphism from boundary measurements given by the hyperbolic Dirichlet-to-Neumann map. This problem is a wave equation analogue of the Calderón problem on Riemannian manifolds. We prove that if a globally hyperbolic metric agrees with the Minkowski metric outside a compact set and has the same hyperbolic Dirichlet-to-Neumann map as the Minkowski metric, then it must be the Minkowski metric up to diffeomorphism. In fact this follows from a stronger result that solves a formally determined inverse problem with a much smaller amount of measurements. To prove these results we introduce a new method for geometric hyperbolic inverse problems. The method is based on distorted plane wave solutions and on a combination of geometric, topological and unique continuation arguments.
SN  - 2692-3688
ER  -