Isospectral convex domains in the hyperbolic plane

Gordon, Carolyn S.; Webb, David L.

doi:10.1090/S0002-9939-1994-1181165-0

Isospectral convex domains in the hyperbolic plane
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by Carolyn S. Gordon and David L. Webb PDF

Proc. Amer. Math. Soc. 120 (1994), 981-983 Request permission

Abstract:

We construct pairs of nonisometric convex polygons in the hyperbolic plane for which the Laplacians are both Dirichlet and Neumann isospectral. We also give examples of pairs of isospectral potentials for the Schrödinger operator on certain convex hyperbolic polygons.

References

Pierre Bérard, Transplantation et isospectralité. I, Math. Ann. 292 (1992), no. 3, 547–559 (French). MR 1152950, DOI 10.1007/BF01444635

Domaines plans isospectraux a la Gordon-Webb-Wolpert

une preuve terre a terre

Peter Buser, John Conway, Peter Doyle, and Klaus-Dieter Semmler, Some planar isospectral domains, Internat. Math. Res. Notices 9 (1994), 391ff., approx. 9 pp.}, issn=1073-7928, review= MR 1301439, doi=10.1155/S1073792894000437,
Carolyn Gordon, David L. Webb, and Scott Wolpert, One cannot hear the shape of a drum, Bull. Amer. Math. Soc. (N.S.) 27 (1992), no. 1, 134–138. MR 1136137, DOI 10.1090/S0273-0979-1992-00289-6
C. Gordon, D. Webb, and S. Wolpert, Isospectral plane domains and surfaces via Riemannian orbifolds, Invent. Math. 110 (1992), no. 1, 1–22. MR 1181812, DOI 10.1007/BF01231320
Mark Kac, Can one hear the shape of a drum?, Amer. Math. Monthly 73 (1966), no. 4, 1–23. MR 201237, DOI 10.2307/2313748
Toshikazu Sunada, Riemannian coverings and isospectral manifolds, Ann. of Math. (2) 121 (1985), no. 1, 169–186. MR 782558, DOI 10.2307/1971195
Hajime Urakawa, Bounded domains which are isospectral but not congruent, Ann. Sci. École Norm. Sup. (4) 15 (1982), no. 3, 441–456. MR 690649