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