Venkat Krishnan
UW
Date: March 1, 2004
We will discuss in this talk a recent article by V. Sharafutdinov. An important problem in Integral Geometry is to recover the solenoidal part of a symmetric tensor field on a compact Riemannian manifold with boundary (M,g) from the knowledge of the integrals of f over all geodesics joining boundary points. The problem has been solved for a large class of manifolds and in all these cases, the boundary of M was assumed to be strictly convex. In this paper, M (with boundary of M not necessarily convex) is a smooth domain inside a compact Riemannian manifold N with strictly convex boundary and the solenoidal part of a symmetric tensor field in N satisfies a stability estimate. With these assumptions we get a solution to the above problem for (M,g).