A support theorem for the X-ray transform on manifolds with plane covers

DOI10.1017/S0305004119000148zbMath1478.53122arXiv1801.06472OpenAlexW2784367186WikidataQ128026972 ScholiaQ128026972MaRDI QIDQ4958655

Norbert Peyerimhoff, Evangelia Samiou

Publication date: 14 September 2021

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.06472

zbMATH Keywords

Heisenberg groupRiemannian manifoldsupport theoremX-ray transformEuclidean planes

Mathematics Subject Classification ID

Radon transform (44A12) Nilpotent and solvable Lie groups (22E25) Integral geometry (53C65)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Tensor tomography on surfaces
• The geometry of filiform nilpotent Lie groups
• X-ray transform on Damek-Ricci spaces
• Tensor tomography: progress and challenges
• L\({}^ p\) harmonic analysis and Radon transforms on the Heisenberg group
• A support theorem for the geodesic ray transform on functions
• Integral geometry of tensor fields on a manifold of negative curvature
• Support of Radon transforms
• Generalized Heisenberg groups and Damek-Ricci harmonic spaces
• 2-step nilpotent Lie groups of higher rank
• Tensor tomography in periodic slabs
• Integral geometry for tensor fields. Transl. from the Russian
• The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds
• X-ray transform on a symmetric space
• The inverse problem for the local geodesic ray transform
• On Radon transforms on compact Lie groups
• Integral Geometry and Radon Transforms
• Geodesics on open surfaces containing horns
• On the kernel of the maximal flat Radon transform on symmetric spaces of compact type
• Tensor tomography on Cartan–Hadamard manifolds
• A duality in integral geometry; some generalizations of the Radon transform
• The Radon Transform and Medical Imaging
• The Mathematics of Medical Imaging