Inverse scattering on conformally compact manifolds

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

Inverse scattering on conformally compact manifolds

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

Abstract
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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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