We discuss the stationary scattering theory on a manifold with "expanding" ends
such as asymptotically Euclidean or asymptotically hyperbolic (funnel) ends.
The main ingredients of the theory are the following:
0. Our formulation of expanding ends
1. Absence of $B_0^*$-eigenfunctions
2. Limiting absorption principle (LAP)
3. Radiation condition bound and Sommerfeld's uniqueness
4. Construction of Fourier transform
5. Stationary scattering matrix and asymptotic behavior of $B^*$-eigenfunctions
In this talk we would like to put an emphasis on the physical picture each
statement describes rather than a technical detail of the proof.
This talk is based on a joint work with Erik Skibsted (Aarhus University).