Some planar isospectral domains

2010/05/11 by Peter Buser, John Conway, Buser, Peter +5
Mathematics · #58J53 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:58J53

paper · pdf · doi:10.48550/arxiv.1005.1839

Version 1.0.1 dated 15 September 1994

arxiv created 2010/05/11 · arxiv updated 2015/03/16

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.

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