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 $\Box + q$, $\rho \partial_t^2 - \Delta$ or $\partial_t^2 - \Delta_g$, for a real smooth function $q(x)$, a positive function $\rho(x)$, or a Riemannian metric $g(x)$ on $\mathbb{R}^n$, with $q, \rho-1, g-g_{Eucl}$ supported in 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 partial results about the recovery of $q,\rho,g$ from these boundary measurements. These are long standing formally determined open problems. These results were obtained in collaboration with Lauri Oksanen and Mikko Salo.
