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One Cannot Hear the Shape of a Drum
Author(s):
Carolyn
Gordon;
David
L.
Webb;
Scott
Wolpert
Journal:
Bull. Amer. Math. Soc.
27
(1992),
134-138.
MSC (1991):
Primary 58G25, 35P05, 53C20
MathSciNet review:
1136137
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References:
- [1]
- P. B\'erard, Transplantation et isospectralit\'e. {\rm I, II}, Math. Ann. MR 1152950
- [2]
- P. B\'erard, \emph{Vari\'et\'es Riemanniennes isospectrales non isometriques} vol.~705, 1988/89. MR 1040571
- [3]
- M. Berger, P. Gauduchon, and E. Mazet, \emph{Le spectre d'une vari\'et\'e riemannienne} vol.~194, Springer-Verlag, 1971. MR 282313
- [4]
- R. Brooks, Constructing isospectral manifolds, Amer. Math. Monthly \textbf{95} (1988), 823--839. MR 967343
- [5]
- R. Brooks, On manifolds of negative curvature with isospectral potentials, Topology \textbf{26} (1987), 63--66. MR 880508
- [6]
- R. Brooks and R. Tse, Isospectral surfaces of small genus, Nagoya Math. J. \textbf{107} (1987), 13--24. MR 909246
- [7]
- P. Buser, Isospectral Riemann surfaces, Ann. Inst. Fourier (Grenoble) \textbf{36} (1986), 167--192. MR 850750
- [8]
- P. Buser, \emph{Cayley graphs and planar isospectral domains}, Proc. Taniguchi Sympos. Geometry and Analysis on Manifolds 1987 vol.~1339, Springer-Verlag, 1988 pp.~64--77. MR 961473
- [9]
- I. Chavel, Eigenvalues in Riemannian geometry, Academic Press, New York, 1984. MR 768584
- [10]
- D. DeTurck, Audible and inaudible geometry properties, Rendicotti Sem. della Faculta di Scienze dell' Univ. di Cagliari \textbf{58 \nofrills}, (1988 supplement): Proc. Conf. on Geometry and Topology, 1--26. MR 1122855
- [11]
- D. DeTurck and C. Gordon, Isospectral deformations. {\rm I}, Riemannian structures on two-step nilspaces, Comm. Pure Appl. Math. \textbf{40} (1987), 367--387. MR 882070
- [12]
- D. DeTurck and C. Gordon, Isospectral deformations. {\rm II}, Trace formulas, metrics, and potentials, Comm. Pure Appl. Math. \textbf{42} (1989), 1067--1095. MR 1029118
- [13]
- C. Gordon, When you can't hear the shape of a manifold, Math. Intelligencer \textbf{11} (1989), 39--47. MR 1007037
- [14]
- C. Gordon and E. Wilson, Isospectral deformations of compact solvmanifold, J. Differential Geom. \textbf{19} (1984), 241--256. MR 739790
- [15]
- A. Ikeda, On lens spaces which are isospectral but not isometric, Ann. Sci. \'Ecole Norm. Sup. (4) \textbf{13} (1980), 303--315. MR 597742
- [16]
- M. Kac, Can one hear the shape of a drum{\rm ?} \nofrills, Amer. Math. Monthly \textbf{73} (1966), 1--23. MR 201237
- [17]
- J. Milnor, Eigenvalues of the Laplace operator on certain manifolds, Proc. Nat. Acad. Sci. U.S.A. \textbf{51} (1964). MR 162204
- [18]
- G. P. Scott, The geometries of 3-manifolds, Bull. London Math. Soc. \textbf{15} (1983), 401--487. MR 705527
- [19]
- T. Sunada, Riemannian coverings and isospectral manifolds, Ann. of Math. (2) \textbf{121} (1985), 169--186. MR 782558
- [20]
- W. P. Thurston, The geometry and topology of \RM 3-manifolds, mimeographed lecture notes, Princeton Univ., 1976--79. MR
- [21]
- H. Urakawa, Bounded domains which are isospectral but not congruent, Ann. Sci. \'Ecole Norm. Sup. (4) \textbf{15} (1982), 441--456. MR 690649
- [22]
- M. F. Vign\'eras, Vari\'et\'es riemanniennes isospectrales et non isom\'etriques, Ann. of Math. (2) \textbf{112} (1980), 21--32. MR 584073
- [23]
- H. Weyl, \"Uber die Asymptotische Verteilung der Eigenwerte, Nachr. Konigl. Ges. Wiss. G\"ottingen (1911), 110--117. MR
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Additional Information:
DOI:
10.1090/S0273-0979-1992-00289-6
PII:
S 0273-0979(1992)00289-6
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