The light ray transform on Lorentzian manifolds

DOI10.1007/S00220-020-03703-6zbMath1452.44006arXiv1907.02210OpenAlexW3104638176MaRDI QIDQ2191176

Lauri Oksanen, Gunther Uhlmann, Matti Lassas, Plamen D. Stefanov

Publication date: 24 June 2020

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.02210

zbMATH Keywords

Lorentzian manifoldweighted light ray transform

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Pseudodifferential and Fourier integral operators on manifolds (58J40) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (8)

Global recovery of a time-dependent coefficient for the wave equation from a single measurement ⋮ Some integral geometry problems for wave equations ⋮ A uniqueness result for light ray transform on symmetric 2-tensor fields ⋮ Inverse problems for real principal type operators ⋮ Travel time tomography in stationary spacetimes ⋮ The light ray transform in stationary and static Lorentzian geometries ⋮ On the light ray transform of wave equation solutions ⋮ Recovery of singularities for the weighted cone transform appearing in Compton camera imaging

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stability estimates for the anisotropic wave equation from the Dirichlet-to-Neumann map
• Property C and an inverse problem for a hyperbolic equation
• Local Lens rigidity with incomplete data for a class of non-simple Riemannian manifolds
• Composition of some singular Fourier integral operators and estimates for restricted X-ray transforms
• An inverse problem for the wave equation
• Full-wave invisibility of active devices at all frequencies
• Uniqueness of the multi-dimensional inverse scattering problem for time dependent potentials
• Nonlocal inversion formulas for the X-ray transform
• On nonuniqueness for Calderón's inverse problem
• The inverse problem for the Dirichlet-to-Neumann map on Lorentzian manifolds
• Inverse problems for Lorentzian manifolds and non-linear hyperbolic equations
• Parametrices for the light ray transform on Minkowski spacetime
• Support theorem for the light-ray transform of vector fields on Minkowski spaces
• On the microlocal analysis of the geodesic X-ray transform with conjugate points
• Stability estimates for the \(X\)-ray transform of tensor fields and boundary rigidity
• The geodesic X-ray transform with fold caustics
• The geodesic ray transform on Riemannian surfaces with conjugate points
• On the inverse problem of finding cosmic strings and other topological defects
• Fourier integral operators. I
• Estimates for singular Radon transforms and pseudodifferential operators with singular symbols
• Boundary rigidity with partial data
• Stable Determination of X-Ray Transforms of Time Dependent Potentials from Partial Boundary Data
• Support theorems for the light ray transform on analytic Lorentzian manifolds
• Globally hyperbolic spacetimes can be defined as ‘causal’ instead of ‘strongly causal’
• Stability estimate for a hyperbolic inverse problem with time-dependent coefficient
• On the cloaking effects associated with anomalous localized resonance
• The attenuated geodesic x-ray transform
• Active Exterior Cloaking for the 2D Laplace and Helmholtz Equations
• Stable Determination of a Simple Metric, a Covector Field and a Potential from the Hyperbolic Dirichlet-to-Neumann Map
• Invisibility and inverse problems
• Determination of time-dependent coefficients for a hyperbolic inverse problem
• Recovery of Time-Dependent Coefficient on Riemannian Manifold for Hyperbolic Equations

This page was built for publication: The light ray transform on Lorentzian manifolds