One cannot hear the shape of a drum

Gordon, Carolyn; Webb, David L.; Wolpert, Scott

doi:10.1090/S0273-0979-1992-00289-6

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ISSN 1088-9485(online) ISSN 0273-0979(print)

One cannot hear the shape of a drum

Authors: Carolyn Gordon, David L. Webb and Scott Wolpert
Journal: Bull. Amer. Math. Soc. 27 (1992), 134-138
MSC (2000): Primary 58G25; Secondary 35R30
MathSciNet review: 1136137
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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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