Some planar isospectral domains
By P. Buser, J. Conway, P. Doyle, Klaus-Dieter Semmler. 2010
129 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Applied Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/d19ee79dfb051bb5ab9f4e0f7fe5ee4579876d64
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In Algebra and Number Theory
In Applied Mathematics
- Iosif Polterovich
- R. Benguria
- Steve Zelditch
- M. Ashbaugh
- Nikolai Nadirashvili
- Dmitry Jakobson
- A. Girouard
- G. Kokarev
Citations in the corpus
- SPECTRAL GEOMETRY OF THE STEKLOV PROBLEM (2014, unknown): “Note that the standard transplantation techniques (see [10, 17, 18]) are not applicable for the Steklov problem, as it is not clear how to “reflect” Steklov eigenfunctions across the boundary.”
- Isoperimetric Inequalities for Eigenvalues of the Laplacian (2007, background): “, the review article of Robert Brooks (1988) with the situation on isospectrality up to that date in [25] (see also, [27]).”
- Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids (2006, background): “2 shows two isospectral planar domains found by Buser et al. [16].”
- Spectral determination of analytic bi-axisymmetric plane domains (2000, background): “In [GWW], [ BuCDS ], many counterexamples are constructed to the question ‘can you hear the shape of a drum’? However, they are all domains with corners.”
- Spectral problems with mixed Dirichlet-Neumann boundary conditions: isospectrality and beyond (2004, methodology): “For arbitrary planar domains it was answered negatively in [14] using an algebraic construction of [22]; see also reviews and extensions [6,4,5] and references therein.”