The geodesic ray transform on spherically symmetric reversible Finsler manifolds

DOI10.1007/s12220-022-01182-wOpenAlexW4321783188MaRDI QIDQ2688859

Keijo Mönkkönen, Joonas Ilmavirta

Publication date: 6 March 2023

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.16886

zbMATH Keywords

inverse problemsintegral geometrygeodesic ray transform

Mathematics Subject Classification ID

Inverse problems in geophysics (86A22) Radon transform (44A12) Classical differential geometry (53A99)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Tensor tomography on surfaces
• Tensor tomography: progress and challenges
• Rigidity and the distance between boundary points
• The X-ray transform for a generic family of curves and weights
• The weighted Doppler transform
• Integral geometry of tensor fields on a manifold of negative curvature
• Planes for which the lines are the shortest paths between points
• The inverse problem of determining a source in the stationary transport equation for a Hamiltonian system
• Seismic rays as Finsler geodesics.
• The X-ray transform on a general family of curves on Finsler surfaces
• Inverting the local geodesic X-ray transform on tensors
• Integral geometry of a tensor field on a surface of revolution
• Integral geometry for tensor fields. Transl. from the Russian
• The attenuated ray transform for connections and Higgs fields
• Local monotonicity of Riemannian and Finsler volume with respect to boundary distances
• A sharp stability estimate for tensor tomography in non-positive curvature
• Travel time tomography
• The geodesic ray transform on Riemannian surfaces with conjugate points
• Two dimensional compact simple Riemannian manifolds are boundary distance rigid
• The inverse problem for the local geodesic ray transform
• A foliated and reversible Finsler manifold is determined by its broken scattering relation
• Spectral rigidity for spherically symmetric manifolds with boundary
• Boundary-rigidity of projective metrics and the geodesic X-ray transform
• Boundary rigidity with partial data
• Numerical Implementation of Geodesic X-Ray Transforms and Their Inversion
• Integral Geometry and Radon Transforms
• Ray tracing in factorized anisotropic inhomogeneous media
• 4. Integral geometry on manifolds with boundary and applications
• Finsler geometry of seismic ray path in anisotropic media
• A note on pseudo-metrics on the plane
• The attenuated geodesic x-ray transform
• Abel transforms with low regularity with applications to x-ray tomography on spherically symmetric manifolds
• Tensor tomography on Cartan–Hadamard manifolds
• Broken ray tomography in the disc
• Inverting the local geodesic ray transform of higher rank tensors
• Generic uniqueness and stability for the mixed ray transform
• Boundary rigidity for Randers metrics
• Geometric Inverse Problems
• Mixed ray transform on simple 2-dimensional Riemannian manifolds
• Global aspects of Finsler geometry
• Pestov identities and X-ray tomography on manifolds of low regularity

This page was built for publication: The geodesic ray transform on spherically symmetric reversible Finsler manifolds