One cannot hear the shape of a drum

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

One cannot hear the shape of a drum

Authors

Gordon, Carolyn

Webb, David L.

Wolpert, Scott

Description

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.
5 pages