One cannot hear the shape of a drum

Preprint

1 July 1992

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/9207215

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

ANSWERING NEGATIVELY
CONNECTED EXAMPLES
CONNECTED MANIFOLD
SIMPLY CONNECTED
CONSTRUCT SIMPLY
HEAR THE SHAPE
ORBIFOLD
DRUM

All Related Versions

Version 1, 1992-07-01, ArXiv

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