Inventiones mathematicae

, Volume 193, Issue 1, pp 229–247

Tensor tomography on surfaces

  • Gabriel P. Paternain
  • Mikko Salo
  • Gunther Uhlmann
Article

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

Abstract

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.

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