English

One cannot hear the shape of a drum

Differential Geometry 2008-02-03 v1

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.

Cite

@article{arxiv.math/9207215,
  title  = {One cannot hear the shape of a drum},
  author = {Carolyn Gordon and David L. Webb and Scott Wolpert},
  journal= {arXiv preprint arXiv:math/9207215},
  year   = {2008}
}

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5 pages