Title: The linearized Calderon problem in transversally anisotropic geometries,
Abstract: In this article we study the linearized anisotropic Calderon problem. In a
compact manifold with boundary, this problem amounts to showing that products
of harmonic functions form a complete set. Assuming that the manifold is
transversally anisotropic, we show that the boundary measurements determine an
FBI type transform at certain points in the transversal manifold. This leads to
recovery of transversal singularities in the linearized problem. The method
requires a geometric condition on the transversal manifold related to pairs of
intersecting geodesics, but it does not involve the geodesic X-ray transform
which has limited earlier results on this problem.