This is a preview of subscription content, access via your institution.
References
[Be1] Bérard, P.: Variétés Riemanniennes isospectrales non isométriques. Astérisque177–178, 127–154 (1989)
[Be2] Bérard, P.: Transplantation et isospectralité I. Math. Ann.292, 547–559 (1992)
[Br1] Brooks, R.: Constructing isospectral manifolds. Am. Math. Mon.95, 823–839 (1988)
[Br2] Brooks, R.: On manifolds of negative curvature with isospectral potentials. Topology26, 63–66 (1987)
[BPY] Brooks, R., Perry, P., Yang, P.: Isospectral sets of conformally equivalent metrics. Duke Math. J.58, 131–150 (1989)
[BT] Brooks, R., Tse, R.: Isospectral surfaces of small genus. Nagoya Math. J.107, 13–24 (1987)
[Bu1] Buser, P.: Cayley graphs and planar isospectral domains. In: Sunada, T. (ed.) Proc. Taniguchi Symp. Geometry and analysis on manifolds, 1987. (Lect. Notes Math., vol. 1339, pp. 64–77.) Berlin Heidelberg New York: Springer 1988
[Bu2] Buser, P.: Isospectral Riemann surfaces. Ann. Inst. Fourier36(2), 167–192 (1986)
[BS] Buser, P., Semmler, K.D.: Private communication
[CF] Cassels, J.W.S., Fröhlich, A.: Algebraic Number Theory. London: Academic Press 1967
[C] Chavel, I.: Eigenvalues in Riemannian Geometry. Academic Press, London 1984
[D] DeTurck, D.: Audible and inaudible geometric properties. Proc. of Conference on Geometry and Topology. In: (Rend. Semin. Fac. Sci. Univ. Cagliari, vol. 58, pp. 1–26 (1988 supplement)) Universita di Cagliari 1988
[DG] DeTurck, D., Gordon, C.: Isospectral deformations II: trace formulas, metrics, and potentials. Commun. Pure Appl. Math.42, 1067–1095 (1989)
[Ga] Gassmann, F.: Bemerkung zu der vorstehenden Arbeit von Hurwitz. Math. Z.25, 124–143 (1926)
[Ge] Gerst, I.: On the theory ofn th power residues and a conjecture of Kronecker. Acta Arithmetica17, 121–139 (1970)
[Go] Gordon, C.: When you can't hear the shape of a manifold. Math. Intell.11, 39–47 (1989)
[GWW] Gordon, C., Webb, D., Wolpert, S.: One can't hear the shape of a drum. Bull. Am. Math. Soc.27, 134–138 (1992).
[Gu] Guralnik, R.: Subgroups inducing the same permutation representation. J. Algebra81, 312–319 (1983)
[K] Kac, M.: Can one hear the shape of a drum? Am. Math. Mon.73, 1–23 (1966)
[P] Perlis, R.: On the equation 22-1. J. Number Theory9, 342–360 (1977)
[Sa] Satake, I.: On a generalization of the notion of manifold. Proc. Natl. Acad. Sci., USA42, 359–363 (1956)
[Sc] Scott, G.P.: The geometries of 3-manifolds. Bull. Lond. Math. Soc.15, 401–487 (1983)
[Su] Sunada, T.: Riemannian coverings and isospectral manifolds. Ann. Math.121, 248–277 (1985)
[T] Thurston, W.P.: The geometry and topology of 3-manifolds. (Mimeographed lecture notes) Princeton University 1976–79
Author information
Authors and Affiliations
Additional information
Oblatum 7-IV-1992
All three authors were partially supported by grants from the National Science Foundation
Rights and permissions
About this article
Cite this article
Gordon, C., Webb, D. & Wolpert, S. Isospectral plane domains and surfaces via Riemannian orbifolds. Invent Math 110, 1–22 (1992). https://doi.org/10.1007/BF01231320
Issue Date:
DOI: https://doi.org/10.1007/BF01231320
Keywords
- Plane Domain
- Riemannian Orbifolds