One cannot hear the shape of a drum
- 1 July 1992
- journal article
- Published by American Mathematical Society (AMS) in Bulletin of the American Mathematical Society
- Vol. 27 (1) , 134-138
- https://doi.org/10.1090/s0273-0979-1992-00289-6
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.Keywords
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