Non-Scattering Energies and Transmission Eigenvalues in Hn

Emilia Blåsten, Esa Vesalainen

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    Sammanfattning

    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.
    OriginalspråkEngelska
    TidskriftAnnales Academiae Scientiarum Fennicae. Mathematica
    Volym45
    Utgåva1
    DOI
    StatusPublicerad - 2020
    MoE-publikationstypA1 Tidskriftsartikel-refererad

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