Title
The fixed angle inverse scattering problem for Riemannian metrics
Abstract
Wave propagation in an inhomogeneous acoustic medium may be modeled, for example, by the wave operators ρ∂t2-∆ or ∂t2-∆g, for a positive function ρ(x) on Rn or a Riemannian metric g(x) on Rn, with ρ=1 or g=gEucl outside a ball. The medium is probed by plane waves coming from a finite number (dimension dependent) of directions, and the resultant time dependent waves are measured on the boundary of the ball. We describe our results about the recovery of ρ,g from
these boundary measurements. These are long standing formally determined open problems. These results were obtained in collaboration with Lauri Oksanen and Mikko Salo.
