Scattering Theory on Geometrically Finite Quotients with Rational Cusps

Abstract

We study Eisenstein functions and scattering operator on geometrically finite hyperbolic manifolds with infinite volume and ‘rational‘ non-maximal rank cusps. For both we prove the meromorphic extension and we show that the scattering operator belongs to a certain class of pseudo-differential operators on the conformal infinity which is a manifold with fibred boundaries.