On the Nodal Count for Flat Tori
نویسندگان
چکیده
We give an explicit formula for the number of nodal domains of certain eigenfunctions on a flat torus. We apply this to an isospectral but not isometric family of pairs of flat four-dimensional tori constructed by Conway and Sloane, and we show that corresponding eigenfunctions have the same number of nodal domains. This disproves a conjecture by Brüning, Gnutzmann, and Smilansky.
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Resolving isospectral ‘drums’ by counting nodal domains
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