Given a smooth non-trapping compact manifold with strictly convex boundary, we consider an inverse problem of reconstructing the manifold from the scattering data initiated from internal sources. These data consist of the exit directions of geodesics that are emaneted from interior points of the manifold. We show that under certain generic assumption of the metric, the scattering data measured on the boundary determine the Riemannian manifold up to isometry.
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Figure 2.
Here is a visualization of the set up in the definition of the function
Figure 4.
Here is a schematic picture about the map
Figure 5.
Here is a schematic picture about the situation where the boundary normal geodesic
Figure 6.
Here is a schematic picture about the map
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