Local Marked Boundary Rigidity Under Hyperbolic Trapping Assumptions

  • Thibault LefeuvreEmail author


Under the assumption that the X-ray transform over symmetric solenoidal 2-tensors is injective, we prove that smooth compact connected manifolds with strictly convex boundary, no conjugate points, and a hyperbolic trapped set are locally marked boundary rigid.


Inverse problem Geodesic flow X-ray transform Boundary rigidity Marked boundary distance function 

Mathematics Subject Classification

37D20 37D40 35R30 



We warmly thank Colin Guillarmou for fruitful discussions during the redaction of this paper. We are also grateful to the anonymous referee for helpful comments. This research is partially supported by the ERC IPFLOW project.


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Authors and Affiliations

  1. 1.Laboratoire de Mathématiques d’Orsay, Univ. Paris-Sud, CNRSUniversité Paris-SaclayOrsayFrance

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