Inventiones mathematicae

, Volume 193, Issue 1, pp 229–247

Tensor tomography on surfaces


  • Gabriel P. Paternain
    • Department of Pure Mathematics and Mathematical StatisticsUniversity of Cambridge
  • Mikko Salo
    • Department of Mathematics and StatisticsUniversity of Jyväskylä
    • Department of MathematicsUniversity of Washington
    • Department of MathematicsUniversity of California

DOI: 10.1007/s00222-012-0432-1

Cite this article as:
Paternain, G.P., Salo, M. & Uhlmann, G. Invent. math. (2013) 193: 229. doi:10.1007/s00222-012-0432-1


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.

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© Springer-Verlag Berlin Heidelberg 2012