Inventiones mathematicae

, Volume 178, Issue 1, pp 119–171

Limiting Carleman weights and anisotropic inverse problems

  • David Dos Santos Ferreira
  • Carlos E. Kenig
  • Mikko Salo
  • Gunther Uhlmann

DOI: 10.1007/s00222-009-0196-4

Cite this article as:
Dos Santos Ferreira, D., Kenig, C.E., Salo, M. et al. Invent. math. (2009) 178: 119. doi:10.1007/s00222-009-0196-4


In this article we consider the anisotropic Calderón problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig et al. (Ann. Math. 165:567–591, 2007) in the Euclidean case. We characterize those Riemannian manifolds which admit limiting Carleman weights, and give a complex geometrical optics construction for a class of such manifolds. This is used to prove uniqueness results for anisotropic inverse problems, via the attenuated geodesic ray transform. Earlier results in dimension n≥3 were restricted to real-analytic metrics.

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • David Dos Santos Ferreira
    • 1
  • Carlos E. Kenig
    • 2
  • Mikko Salo
    • 3
  • Gunther Uhlmann
    • 4
  1. 1.LAGA, MathématiqueUniversité Paris 13VilletaneuseFrance
  2. 2.Department of MathematicsUniversity of ChicagoChicagoUSA
  3. 3.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  4. 4.Department of MathematicsUniversity of WashingtonSeattleUSA

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