Non-Scattering Energies and Transmission Eigenvalues in Hn

Emilia Blåsten, Esa Vesalainen

    Research output: Contribution to journalArticlepeer-review

    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 languageEnglish
    JournalAnnales Academiae Scientiarum Fennicae. Mathematica
    Volume45
    Issue number1
    DOIs
    Publication statusPublished - 2020
    MoE publication typeA1 Journal article-refereed

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