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Article Dans Une Revue Mathematische Zeitschrift Année : 2021

One can't hear orientability of surfaces

Pierre Bérard
David L Webb
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Résumé

The main result of this paper is that one cannot hear orientability of a surface with boundary. More precisely, we construct two isospectral flat surfaces with boundary with the same Neumann spectrum, one orientable, the other non-orientable. For this purpose, we apply Sunada's and Buser's methods in the framework of orbifolds. Choosing a symmetric tile in our construction, and adapting a folklore argument of Fefferman, we also show that the surfaces have different Dirichlet spectra. These results were announced in the {\it C. R. Acad. Sci. Paris S\'er. I Math.}, volume 320 in 1995, but the full proofs so far have only circulated in preprint form.
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hal-02937342 , version 1 (13-09-2020)

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Pierre Bérard, David L Webb. One can't hear orientability of surfaces. Mathematische Zeitschrift, 2021, https://doi.org/10.1007/s00209-021-02758-y. ⟨10.1007/s00209-021-02758-y⟩. ⟨hal-02937342⟩
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