Inverse scattering on conformally compact manifolds

Leonardo Marazzi

doi:10.3934/ipi.2009.3.537

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2009, Volume 3, Issue 3: 537-550. Doi: 10.3934/ipi.2009.3.537

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Inverse scattering on conformally compact manifolds

Leonardo Marazzi^1,

1.
Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067

Received: February 29, 2008

Revised: May 31, 2009

Published: July 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 35R30, 35P25; Secondary: 58J40.

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