Scattering rigidity conjecture for compact Riemannian manifolds of Anosov type

Let $M_1$ and $M_2$ be compact Riemannian manifolds of Anosov type, each with scattering data. Scattering rigidity conjecture. If $M_1$ and $M_2$ have the same scattering data, then they are isometric by an isometry fixing the boundary. This conjecture proposes that scattering data determine a compact Riemannian manifold of Anosov type up to an isometry that fixes the boundary, extending the chain of rigidity implications discussed in the paper. Its resolution is not established in the supplied source.