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The Attenuated Geodesic Ray Transform on Tensors: Generic Injectivity and Stability

  • Yernat M. AssylbekovEmail author
Article
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Abstract

We consider the attenuated geodesic ray transform defined on pairs of symmetric 2-tensors and 1-forms on a simple Riemannian manifold. We prove injectivity and stability results for a class of generic simple metrics and attenuations containing real analytic ones. In fact, methods used in this paper can be modified to generalize our results for a class of non-simple manifolds similar to Stefanov and Uhlmann Am J Math 130(1):239–268 (2008).

Keywords

Inverse problems Integral geometry Attenuated geodesic ray transform Tensors 

Mathematics Subject Classification

53C65 35R30 

Notes

Acknowledgements

The author is grateful to Professor Plamen Stefanov for his suggestions on an earlier version of this paper. The work was partially supported by AMS-Simons travel grant.

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Copyright information

© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.Department of Computational Mathematics, Science and EngineeringMichigan State UniversityEast LansingUSA

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