American Institute of Mathematical Sciences

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August  2009, 3(3): 537-550. doi: 10.3934/ipi.2009.3.537

Inverse scattering on conformally compact manifolds

Leonardo Marazzi 1,

1. 

Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067, United States

Received  March 2008 Revised  June 2009 Published  July 2009

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.
Mathematics Subject Classification: Primary: 35R30, 35P25; Secondary: 58J4.
Citation: Leonardo Marazzi. Inverse scattering on conformally compact manifolds. Inverse Problems & Imaging, 2009, 3 (3) : 537-550. doi: 10.3934/ipi.2009.3.537
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