6533b837fe1ef96bd12a1d98

RESEARCH PRODUCT

Tensor tomography on Cartan–Hadamard manifolds

Jere LehtonenJesse RailoMikko Salo

subject

Mathematics - Differential GeometryPure mathematicsGeodesic01 natural sciencesTheoretical Computer ScienceTensor fieldHadamard transform44A12 53C21 53C22 45Q05Euclidean geometryFOS: MathematicsSectional curvatureTensor0101 mathematicsMathematical PhysicsMathematicsCartan-Hadamard manifoldsSolenoidal vector fieldApplied Mathematics010102 general mathematicsComputer Science Applications010101 applied mathematicsDifferential Geometry (math.DG)Bounded functionSignal Processingtensor tomographyMathematics::Differential Geometry

description

We study the geodesic X-ray transform on Cartan-Hadamard manifolds, and prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature decays at infinity. This work extends the results of Lehtonen (2016) to dimensions $n \geq 3$ and to the case of tensor fields of any order.

yearjournalcountryeditionlanguage
2017-05-29Inverse Problems
https://doi.org/10.1088/1361-6420/aaaf85