Inventiones mathematicae

, Volume 193, Issue 1, pp 229–247 | Cite as

Tensor tomography on surfaces

  • Gabriel P. Paternain
  • Mikko Salo
  • Gunther Uhlmann


We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the two-dimensional case.


Tensor Field Carleman Estimate Simple Surface Commutator Formula Canonical Line Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



M.S. was supported in part by the Academy of Finland, and G.U. was partly supported by NSF and a Rothschild Distinguished Visiting Fellowship at the Isaac Newton Institute. The authors would like to express their gratitude to the Newton Institute and the organizers of the program on Inverse Problems in 2011 where this work was carried out. They would also like to thank the referees for their constructive and useful comments.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gabriel P. Paternain
    • 1
  • Mikko Salo
    • 2
  • Gunther Uhlmann
    • 3
    • 4
  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridgeUK
  2. 2.Department of Mathematics and StatisticsUniversity of JyväskyläJyväskyläFinland
  3. 3.Department of MathematicsUniversity of WashingtonSeattleUSA
  4. 4.Department of MathematicsUniversity of CaliforniaIrvineUSA

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