Geodesic X-ray transform on nontrapping manifolds
We have a compact nontrapping manifold with strictly convex boundary and an
unknown function (which is suitably regular enough). It has been conjectured that the
unknown function can be determined from its integrals over geodesics joining
two boundary points. Together with J. Ilmavirta and M. Salo we confirmed this
conjecture in the case of piecewise constant functions in dimension two. In higher
dimensional case we need to assume a certain foliation condition to be satisfied
too. The proof is based on rather elementary geometric arguments.