Inverse Scattering with Partial data on Asymptotically Hyperbolic Manifolds

TL;DR

This paper proves that partial boundary scattering data uniquely determines an asymptotically hyperbolic manifold up to isometries, advancing inverse scattering theory in geometric analysis.

Contribution

It establishes a uniqueness result for inverse scattering on asymptotically hyperbolic manifolds using partial boundary data.

Findings

Partial scattering matrix determines the manifold up to isometry.

Uniqueness holds when scattering data is known on an open boundary subset.

Results extend inverse scattering theory to more general geometric settings.

Abstract

We prove that the scattering matrix at all energies restricted to an open subset of the boundary determines an asymptotically hyperbolic manifold modulo isometries that are equal to the identity on the open subset where the scattering matrix is known.