Inverse scattering on conformally compact manifolds

We study inverse scattering for $Δ_g+V$ on $(X,g)$ a conformally compact manifold with metric $g,$ with variable sectional curvature $-\alf^2(y)$ at the boundary and $V\in C^\infty(X)$ not vanishing at the boundary. We prove that the scattering matrix at a fixed energies $(λ_1,$ $λ_2)$ in a suitable subset of $\mc$, determines $\alf,$ and the Taylor series of both the potential and the metric at the boundary.

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