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
DOI:
https://doi.org/10.1090/S0273-0979-1992-00289-6
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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© Copyright 1992
American Mathematical Society