4 papers
A generalized Helmholtz-type decomposition of symmetric tensor fields and applications to ray transforms
Antti Kykkänen, Rohit Kumar Mishra, Suman Kumar Sahoo
We study a solenoidal-potential type decomposition of a symmetric -tensor field in $\Rb^2$, and its implications to injectivity questions for the momentum and elastic ray transf…
The elastic ray transform
Joonas Ilmavirta, Antti Kykkänen, Teemu Saksala
We introduce and study a new family of tensor tomography problems. At rank 2 it corresponds to linearization of travel time of elastic waves, measured for all polarizations. We pro…
Lipschitz Stability of Travel Time Data
Joonas Ilmavirta, Antti Kykkänen, Matti Lassas +2
We prove that the reconstruction of a certain type of length spaces from their travel time data on a closed subset is Lipschitz stable. The travel time data is the set of distance…
Tensor tomography on negatively curved manifolds of low regularity
Joonas Ilmavirta, Antti Kykkänen
We prove solenoidal injectivity for the geodesic X-ray transform of tensor fields on simple Riemannian manifolds with metrics and non-positive sectional curvature. The pr…