English

Some planar isospectral domains

Differential Geometry 2015-03-17 v1

Abstract

We give a number of examples of isospectral pairs of plane domains, and a particularly simple method of proving isospectrality. One of our examples is a pair of domains that are not only isospectral but homophonic: Each domain has a distinguished point such that corresponding normalized Dirichlet eigenfunctions take equal values at the distinguished points. This shows that one really can't hear the shape of a drum.

Keywords

Cite

@article{arxiv.1005.1839,
  title  = {Some planar isospectral domains},
  author = {Peter Buser and John Conway and Peter Doyle and Klaus-Dieter Semmler},
  journal= {arXiv preprint arXiv:1005.1839},
  year   = {2015}
}

Comments

Version 1.0.1 dated 15 September 1994

R2 v1 2026-06-21T15:21:14.395Z