Scattering and Inverse Scattering on ACH Manifolds

Colin Guillarmou (1) , Antonio Sa Barreto (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 Purdue University [West Lafayette]

We study scattering and inverse scattering theories for asymptotically complex hyperbolic manifolds. We show the existence of the scattering operator as a meromorphic family of operators in the Heisenberg calculus on the boundary, which is a contact manifold with a pseudohermitian structure. Then we define the radiation fields as in the real asymptotically hyperbolic case, and reconstruct the scattering operator from those fields. As an application we show that the manifold, including its topology and the metric, are determined up to invariants by the scattering matrix at all energies.

Domaines: Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Colin Guillarmou, Antonio Sa Barreto. Scattering and Inverse Scattering on ACH Manifolds. Journal für die reine und angewandte Mathematik, 2008, 622, pp.1-55. ⟨hal-00250141⟩