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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On hearing the shape of a triangle


Authors: Pei-Kun Chang and Dennis DeTurck
Journal: Proc. Amer. Math. Soc. 105 (1989), 1033-1038
MSC: Primary 58G25; Secondary 35P99, 35R30
MathSciNet review: 953738
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Abstract: To determine whether two triangles in the Euclidean plane are congruent, it suffices to know that they have their first $ N$ eigenvalues in common, where $ N$ depends on the first two eigenvalues of the triangles. Similar results for other figures are given.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0953738-7
PII: S 0002-9939(1989)0953738-7
Keywords: Eigenvalues of Laplacian, inverse spectral problem
Article copyright: © Copyright 1989 American Mathematical Society