Inverting the local geodesic X-ray transform on tensors

DOI10.1007/s11854-018-0058-3OpenAlexW2963168736WikidataQ114221663 ScholiaQ114221663MaRDI QIDQ1713990

Gunther Uhlmann, András Vasy, Plamen D. Stefanov

Publication date: 30 January 2019

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.5145

Mathematics Subject Classification ID

Miscellaneous topics in partial differential equations (35Rxx) Hyperbolic equations and hyperbolic systems (35Lxx)

Related Items (35)

The X-ray transform for connections in negative curvature ⋮ Lens rigidity with partial data in the presence of a magnetic field ⋮ Recovery of Piecewise Smooth Density and Lamé Parameters from High Frequency Exterior Cauchy Data ⋮ Inverse problems for magnetic Schrödinger operators in transversally anisotropic geometries ⋮ The attenuated geodesic x-ray transform ⋮ Reconstruction of a compact manifold from the scattering data of internal sources ⋮ The geodesic ray transform on spherically symmetric reversible Finsler manifolds ⋮ Inverse problems for nonlinear magnetic Schrödinger equations on conformally transversally anisotropic manifolds ⋮ Calderón problem for connections ⋮ The Local Magnetic Ray Transform of Tensor Fields ⋮ X-ray transform and boundary rigidity for asymptotically hyperbolic manifolds ⋮ Numerical Solution of a Linearized Travel Time Tomography Problem With Incomplete Data ⋮ Lens rigidity for a particle in a Yang-Mills field ⋮ Invariant distributions, Beurling transforms and tensor tomography in higher dimensions ⋮ Full reconstruction of a vector field from restricted Doppler and first integral moment transforms in \(\mathbb{R}^n\) ⋮ Towards bulk metric reconstruction from extremal area variations ⋮ Injectivity and stability for a generic class of generalized Radon transforms ⋮ The light ray transform in stationary and static Lorentzian geometries ⋮ Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge ⋮ A sharp stability estimate for tensor tomography in non-positive curvature ⋮ Sharp stability estimate for the geodesic ray transform ⋮ The ball-based origami theorem and a glimpse of holography for traversing flows ⋮ The attenuated geodesic ray transform on tensors: generic injectivity and stability ⋮ Conditionally stable unique continuation and applications to thermoacoustic tomography ⋮ Inverting the local geodesic ray transform of higher rank tensors ⋮ The ray transform of symmetric tensor fields with incomplete projection data. I: The kernel of the ray transform ⋮ Travel time tomography ⋮ On the travel time tomography problem in 3D ⋮ Mixed ray transform on simple 2-dimensional Riemannian manifolds ⋮ X-ray Tomography of One-forms with Partial Data ⋮ Well-defined forward operators in dynamic diffractive tensor tomography using viscosity solutions of transport equations ⋮ Unique continuation of the normal operator of the x-ray transform and applications in geophysics ⋮ Recovery of discontinuous Lamé parameters from exterior Cauchy data ⋮ Generic uniqueness and stability for the mixed ray transform ⋮ Inverse Boundary Problems for Biharmonic Operators in Transversally Anisotropic Geometries

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lens rigidity with trapped geodesics in two dimensions
• Tensor tomography on surfaces
• Local Lens rigidity with incomplete data for a class of non-simple Riemannian manifolds
• Variations of Dirichlet-to-Neumann map and deformation boundary rigidity of simple 2-manifolds
• A support theorem for the geodesic ray transform on functions
• Support theorems for real-analytic Radon transforms
• Convexity of spheres in a manifold without conjugate points
• Stability estimates for the \(X\)-ray transform of tensor fields and boundary rigidity
• Integral geometry for tensor fields. Transl. from the Russian
• Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge
• A support theorem for the geodesic ray transform of symmetric tensor fields
• Two dimensional compact simple Riemannian manifolds are boundary distance rigid
• The inverse problem for the local geodesic ray transform
• Boundary rigidity with partial data
• Lens rigidity for manifolds with hyperbolic trapped sets
• On uniqueness of determination of a form of first degree by its integrals along geodesics
• Conjugacy rigidity for non-positively curved graph manifolds
• Scattering rigidity with trapped geodesics
• Integral geometry problem for nontrapping manifolds
• Boundary rigidity and stability for generic simple metrics
• Integral geometry of tensor fields on a class of non-simple Riemannian manifolds

This page was built for publication: Inverting the local geodesic X-ray transform on tensors