Inverse scattering on conformally compact manifolds
Leonardo Marazzi
Inverse Problems & Imaging 2009, 3(3): 537-550 doi: 10.3934/ipi.2009.3.537
We study inverse scattering for $\Delta_g+V$ on $(X,g)$ a conformally compact manifold with metric $g,$ with variable sectional curvature -α2(y) at the boundary and $V\in C^\infty(X)$ not vanishing at the boundary. We prove that the scattering matrices at two fixed energies $\lambda_1,$ $\lambda_2$ in a suitable subset of c , determines α, and the Taylor series of both the potential and the metric at the boundary.
keywords: scattering matrix. Inverse problems conformally compact manifolds

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