Bounded domains which are isospectral but not congruent
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 15 (1982) no. 3, pp. 441-456.
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     author = {Urakawa, Hajime},
     title = {Bounded domains which are isospectral but not congruent},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {441--456},
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     volume = {Ser. 4, 15},
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     year = {1982},
     doi = {10.24033/asens.1433},
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     zbl = {0505.58036},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/asens.1433/}
}
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Urakawa, Hajime. Bounded domains which are isospectral but not congruent. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 15 (1982) no. 3, pp. 441-456. doi : 10.24033/asens.1433. http://archive.numdam.org/articles/10.24033/asens.1433/

[A] S. Agmon, Lecture Notes on Elliptic Boundary Value Problems (van Nostrand Company, Toronto-Princeton-New York-London, 1965). | MR | Zbl

[B1] P. Bérard, Spectres et groupes cristallographiques I: domaines euclidiens (Invent. Math., Vol. 58, 1980, pp. 179-199). | MR | Zbl

[B2] P. Bérard, Remarque sur la conjecture de Weyl (to appear in Compositio Math.). | Numdam

[B.B.] P. Bérard and G. Besson, Spectres et groupes cristallographiques II: domaines sphériques (Ann. Inst. Fourier, Grenoble, Vol. 30, No. 3, 1980, pp. 237-248). | Numdam | MR | Zbl

[Br] M. Berger, Eigenvalues of the Laplacian (Amer. Math. Soc., Proc. Pure Math., Vol. 16, 1970, pp. 121-125). | MR | Zbl

[B.G.M.] M. Berger, P. Gauduchon and E. Mazet, Le spectre d'une variété riemannienne (Lecture Notes in Math., No. 194, Springer-Verlag, Berlin-Heiderberg-New York, 1970). | MR | Zbl

[B.N.] N. Bourbaki, Groupes et algèbres de Lie, Chapitres 4 à 6, Hermann, Paris, 1968.

F. H. Brownell, Extended Asymptotic Eigenvalue Distributions for Bounded Domains in n-Space (J. Math. Mech., Vol. 6, 1957, pp. 119-166). | MR | Zbl

[C] T. Carleman, Über die asymptotische Verteilung der Eigenwerte partieller Differential gleichungen (Ber. der Sachs. Acad. d. Wiss. Leipzig, Vol. 88, 1936, pp. 119-132). | JFM | Zbl

[E] N. Ejiri, A Construction of Non-Flat Compact Irreducible Riemannian Manifolds which are Isospectral But not Isometric (Math. Z., Vol. 168, 1979, pp. 207-212). | EuDML | MR | Zbl

[F] G. Faber, Beweis, dass unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt (Sitz. ber. bayer. Acad. Wiss., 1923, pp. 169-172). | JFM

[Gd] P. Grisvard, Boundary Value Problems in Non-Smooth Domains (Lecture Notes, No. 19, Univ. Maryland, Depart. Math., College Park, 1980).

[G] D. Gromes, Über die asymptotische Verteilung der Eigenwerte des Laplace-Operators fur Gebiete auf der Kugeloberfläche (Math. Z., Vol. 94, 1966, pp. 110-121). | EuDML | MR | Zbl

[I] A. Ikeda, On Lens Spaces which are Isospectral But not Isometric (Ann. scient. Éc. Norm. Sup., 4e série, t. 13, 1980, pp. 303-315). | EuDML | Numdam | MR | Zbl

[K] M. Kac, Can One Hear the Shape of a Drum? (Amer. Math. Monthly, Vol. 73, 1966, pp. 1-23). | MR | Zbl

[Kr] E. Krahn, Ueber Minimaleigenschaften der Kugel in drei und mehr Dimensionen (Acta Comm. Univ. Tartu (Dorpat), Vol. 9, 1926, p. 1-144). | JFM

[M.S.] H. P. Mckean and I. M. Singer, Curvature and the Eigenvalues of the Laplacian (J. Diff. Geometry, Vol. 1, 1967, pp. 43-69). | MR | Zbl

[M] J. Milnor, Eigenvalues of the Laplace Operator on Certain Manifolds (Proc. Nat. Acad. Sc., Vol. 51, 1964, p. 542). | MR | Zbl

[P] H. Prüfer, Neue Herleitung der Sturm-Liouvilleschen Reihenentwicklung stetiger Functionen (Math. Ann., Vol. 95, 1926, pp. 499-518). | EuDML | JFM

[V] M. F. Vignéras, Variétés riemanniennes isospectrales et non isométriques (Ann. Math., Vol. 112, 1980, pp. 21-32). | MR | Zbl

[Wr] H. F. Weinberger, An Isoperimetric Inequality for the N-dimensional Free Membrane Problem (J. Rat. Mech. Anal., Vol. 5, 1956, pp. 533-536). | MR | Zbl

[W] H. Weyl, Das asymptotische Verteilungsgesetz der Eigenschwingungen eines beliebig gestalten elastische Körpers (Rendiconti. Circ. Math. Palermo, Vol. 39, 1915, pp. 1-50). | JFM

[Yau] S. T. Yau, Problem section, Institute for Advanced Study, Princeton (to appear in Annals of Math. Studies).

[Y] K. Yosida, Methods of Solving Differential Equations (in Japanese), 2nd ed. (Iwanami, Tokyo, 1978).

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