Abstract
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.
| Original language | English |
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| Journal | Annales Academiae Scientiarum Fennicae. Mathematica |
| Volume | 45 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2020 |
| MoE publication type | A1 Journal article-refereed |