45 citations · 238 across the 51 of their papers we have counts for
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math.DG2018★ 2 cited
Functions of constant geodesic X-ray transform
Joonas Ilmavirta, Gabriel P. Paternain
We show that the existence of a function in with constant geodesic X-ray transform imposes geometrical restrictions on the manifold. The boundary of the manifold has to be…
math.DG2018★ 1 cited
Integral geometry on manifolds with boundary and applications
Joonas Ilmavirta, François Monard
We survey recent results on inverse problems for geodesic X-ray transforms and other linear and non-linear geometric inverse problems for Riemannian metrics, connections and Higgs…
math.DG2018★ 1 cited
Broken ray tensor tomography with one reflecting obstacle
Joonas Ilmavirta, Gabriel P. Paternain
We show that a tensor field of any rank integrates to zero over all broken rays if and only if it is a symmetrized covariant derivative of a lower order tensor which satisfies a sy…