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Isospectral Riemann surfaces. (English) Zbl 0579.53036

We construct new examples of compact Riemann surfaces which are non isometric but have the same spectrum of the Laplacian. Examples are given for genus \(g=5\) and for all \(g\geq 7\). In a second part we give examples of isospectral non isometric surfaces in \({\mathbb{R}}^ 3\) which are realizable by paper models.

MSC:

53C20 Global Riemannian geometry, including pinching
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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References:

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