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One cannot hear the shape of a drum

Carolyn Gordon·David L. Webb·Scott Wolpert
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Abstract

We use an extension of Sunada's theorem to construct a nonisometric pair of isospectral simply connected domains in the Euclidean plane, thus answering negatively Kac's question, ``can one hear the shape of a drum?'' In order to construct simply connected examples, we exploit the observation that an orbifold whose underlying space is a simply connected manifold with boundary need not be simply connected as an orbifold.

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Carolyn Gordon, David L. Webb, Scott Wolpert. 1992-07-01. One cannot hear the shape of a drum. https://arxiv.org/abs/math/9207215

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