Geometric and Obstacle Scattering at Low Energy

Understand

We consider scattering theory of the Laplace Beltrami operator on differential forms on a Riemannian manifold that is Euclidean at infinity.

• The manifold may have several boundary components caused by obstacles at which relative boundary conditions are imposed.
• Scattering takes place because of the presence of these obstacles and possible non-trivial topology and geometry.
• Unlike in the case of functions eigenvalues generally exist at the bottom of the continuous spectrum and the corresponding eigenforms represent cohomology classes.