%0 Journal Article
%T Some planar isospectral domains
%A Peter Buser
%A John Conway
%A Peter Doyle
%A Klaus-Dieter Semmler
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1005.1839v1