Inventiones mathematicae

, Volume 110, Issue 1, pp 1–22 | Cite as

Isospectral plane domains and surfaces via Riemannian orbifolds

  • C. Gordon
  • D. Webb
  • S. Wolpert


Plane Domain Riemannian Orbifolds 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Be1] Bérard, P.: Variétés Riemanniennes isospectrales non isométriques. Astérisque177–178, 127–154 (1989)Google Scholar
  2. [Be2] Bérard, P.: Transplantation et isospectralité I. Math. Ann.292, 547–559 (1992)Google Scholar
  3. [Br1] Brooks, R.: Constructing isospectral manifolds. Am. Math. Mon.95, 823–839 (1988)Google Scholar
  4. [Br2] Brooks, R.: On manifolds of negative curvature with isospectral potentials. Topology26, 63–66 (1987)Google Scholar
  5. [BPY] Brooks, R., Perry, P., Yang, P.: Isospectral sets of conformally equivalent metrics. Duke Math. J.58, 131–150 (1989)Google Scholar
  6. [BT] Brooks, R., Tse, R.: Isospectral surfaces of small genus. Nagoya Math. J.107, 13–24 (1987)Google Scholar
  7. [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 1988Google Scholar
  8. [Bu2] Buser, P.: Isospectral Riemann surfaces. Ann. Inst. Fourier36(2), 167–192 (1986)Google Scholar
  9. [BS] Buser, P., Semmler, K.D.: Private communicationGoogle Scholar
  10. [CF] Cassels, J.W.S., Fröhlich, A.: Algebraic Number Theory. London: Academic Press 1967Google Scholar
  11. [C] Chavel, I.: Eigenvalues in Riemannian Geometry. Academic Press, London 1984Google Scholar
  12. [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 1988Google Scholar
  13. [DG] DeTurck, D., Gordon, C.: Isospectral deformations II: trace formulas, metrics, and potentials. Commun. Pure Appl. Math.42, 1067–1095 (1989)Google Scholar
  14. [Ga] Gassmann, F.: Bemerkung zu der vorstehenden Arbeit von Hurwitz. Math. Z.25, 124–143 (1926)Google Scholar
  15. [Ge] Gerst, I.: On the theory ofn th power residues and a conjecture of Kronecker. Acta Arithmetica17, 121–139 (1970)Google Scholar
  16. [Go] Gordon, C.: When you can't hear the shape of a manifold. Math. Intell.11, 39–47 (1989)Google Scholar
  17. [GWW] Gordon, C., Webb, D., Wolpert, S.: One can't hear the shape of a drum. Bull. Am. Math. Soc.27, 134–138 (1992).Google Scholar
  18. [Gu] Guralnik, R.: Subgroups inducing the same permutation representation. J. Algebra81, 312–319 (1983)Google Scholar
  19. [K] Kac, M.: Can one hear the shape of a drum? Am. Math. Mon.73, 1–23 (1966)Google Scholar
  20. [P] Perlis, R.: On the equation 22-1. J. Number Theory9, 342–360 (1977)Google Scholar
  21. [Sa] Satake, I.: On a generalization of the notion of manifold. Proc. Natl. Acad. Sci., USA42, 359–363 (1956)Google Scholar
  22. [Sc] Scott, G.P.: The geometries of 3-manifolds. Bull. Lond. Math. Soc.15, 401–487 (1983)Google Scholar
  23. [Su] Sunada, T.: Riemannian coverings and isospectral manifolds. Ann. Math.121, 248–277 (1985)Google Scholar
  24. [T] Thurston, W.P.: The geometry and topology of 3-manifolds. (Mimeographed lecture notes) Princeton University 1976–79Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • C. Gordon
    • 1
    • 2
  • D. Webb
    • 1
    • 2
  • S. Wolpert
    • 3
  1. 1.Department of MathematicsDartmouth CollegeHanoverUSA
  2. 2.USA
  3. 3.Department of MathematicsUniversity of MarylandCollege ParkUSA

Personalised recommendations