Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge

DOI10.4007/annals.2021.194.1.1zbMath1482.53056arXiv1702.03638OpenAlexW3176739557MaRDI QIDQ2042070

András Vasy, Gunther Uhlmann, Plamen D. Stefanov

Publication date: 27 July 2021

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.03638

zbMATH Keywords

microlocal analysislens rigidityboundary rigidityfoliation conditionnormal gauge

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Inverse problems for PDEs (35R30) Integral geometry (53C65) Rigidity results (53C24) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

Boundary rigidity of negatively-curved asymptotically hyperbolic surfaces ⋮ A foliated and reversible Finsler manifold is determined by its broken scattering relation ⋮ Boundary-rigidity of projective metrics and the geodesic X-ray transform ⋮ Uniqueness of the partial travel time representation of a compact Riemannian manifold with strictly convex boundary ⋮ Sampling the X-ray Transform on Simple Surfaces ⋮ Carleman estimates for geodesic X-ray transforms ⋮ The transport Oka-Grauert principle for simple surfaces ⋮ Riemannian Anosov extension and applications ⋮ Inverse problems for real principal type operators ⋮ Marked boundary rigidity for surfaces of Anosov type ⋮ Local recovery of the compressional and shear speeds from the hyperbolic DN map ⋮ Inverting the local geodesic X-ray transform on tensors ⋮ Travel time tomography in stationary spacetimes ⋮ On an inverse boundary value problem for a nonlinear elastic wave equation ⋮ Stability of the non-abelian \(X\)-ray transform in dimension \(\ge 3\) ⋮ Travel time tomography with formally determined incomplete data in 3D ⋮ Recovery of material parameters in transversely isotropic media ⋮ Local marked boundary rigidity under hyperbolic trapping assumptions ⋮ Stitching data: recovering a manifold's geometry from geodesic intersections ⋮ Inverse problems for nonlinear hyperbolic equations with disjoint sources and receivers

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