Resumen de Integral geometry of tensor fields on a class of non-simple Riemannian manifolds

Plamen Stefanov, Gunther Uhlmann

• We study the geodesic X-ray transform IG of tensor fields on a compact Riemannian manifold M with non-necessarily convex boundary and with possible conjugate points. We assume that IG is known for geodesics belonging to an open set G with endpoints on the boundary. We prove generic s-injectivity and a stability estimate under some topological assumptions and under the condition that for any (x,?) ? T*M, there is a geodesic in G through x normal to ? without conjugate points.