Inverse scattering on conformally compact manifolds

Abstract

We study inverse scattering for ${\Delta }_g+V$ 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 $({\lambda }_1,$ ${\lambda }_2)$ in a suitable subset of $\mc$, determines $\alf,$ and the Taylor series of both the potential and the metric at the boundary.

12 pages, more detail added, small corrections

References in corpus (1)

• Determining Asymptotics of Magnetic Fields from Fixed Energy Scattering Data

Cited by in corpus (1)

• Absence of Resonances near Critical Line for CC Manifolds