We consider non-scattering energies and transmission eigenvalues of compactly supported potentials in the hyperbolic spaces H-n. We prove that in H-2 a corner bounded by two hyperbolic lines intersecting at an angle smaller than 180 degrees always scatters, and that one of the lines may be replaced by a horocycle. In higher dimensions, we obtain similar results for corners bounded by hyperbolic hyperplanes intersecting each other pairwise orthogonally, and that one of the hyperplanes may be replaced by a horosphere. The corner scattering results are contrasted by proving discreteness and existence results for the related transmission eigenvalue problems.
|Journal||Annales Academiae Scientiarum Fennicae. Mathematica|
|Publication status||Published - 2020|
|MoE publication type||A1 Journal article-refereed|