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Generic simplicity of ellipses

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arxiv 2403.07377 v2 pith:TE46A46N submitted 2024-03-12 math.SP

Luc Hillairet , Chris M. Judge This is my paper · ORCID
classification math.SP
keywords genericspectrumasymptoticboundarybourgetconditioncorrectdirichlet
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We prove that the Laplace spectrum of the generic ellipse is simple, both with Neumann and Dirichlet boundary condition. We rely on the known multiplicities in the spectrum of the disk (Bourget's hypothesis) and on a refined version of our method of asymptotic separation of variables. In v1, the statement of prop. 2.1 is correct but the proof is not.

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Cited by 1 Pith paper

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  1. Local limits of high energy eigenfunctions on integrable billiards

    math.SP 2025-02 reject novelty 7.0 of 10

    Rational rectangles and the three integrable triangles have strong inverse localization, while generic irrational rectangles and (claimed) generic ellipses fail it strongly.

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