@incollection{SB_1988-1989__31__127_0, author = {B\'erard, Pierre}, title = {Vari\'et\'es riemanniennes isospectrales non isom\'etriques}, booktitle = {S\'eminaire Bourbaki : volume 1988/89, expos\'es 700-714}, author = {Collectif}, series = {Ast\'erisque}, note = {talk:705}, publisher = {Soci\'et\'e math\'ematique de France}, number = {177-178}, year = {1989}, zbl = {0703.53035}, mrnumber = {1040571}, language = {fr}, url = {www.numdam.org/item/SB_1988-1989__31__127_0/} }
Bérard, Pierre. Variétés riemanniennes isospectrales non isométriques, dans Séminaire Bourbaki : volume 1988/89, exposés 700-714, Astérisque, no. 177-178 (1989), Exposé no. 705, 28 p. http://www.numdam.org/item/SB_1988-1989__31__127_0/
[1] Transplantation des fonctions et isospectralité, en préparation.
-[1] Le spectre d'une variété riemannienne en 1982, in Spectra of Riemannian manifolds, Kaigai Publications (1983), 139-194, [Proc. France-Japan 1984 Seminar Kyoto ed. Berger, Murakami, Ochiai], ou dans Lecture Notes in Math. Springer, 1207 (1986).
, -[1] Geometry of the spectrum, Proc. Symp. Pure Math. 27 Part 2, Amer. Math. Soc. 1975, 129-152. | MR 383459 | Zbl 0311.53055
-[1] Le spectre d'une variété riemannienne, Lecture Notes in Math. Springer 194, 1971. | MR 282313 | Zbl 0223.53034
, , -[1] Tores isospectraux en dimension 3, C. R. Acad. Sci. Paris Sér. I Math., 292 (1981), 163-166. | MR 610309 | Zbl 0464.58018
-[1] Determination of a Riemannian metric form the first variation of its spectrum, Amer. J. Math., 107 (1985), 815-831. | MR 796904 | Zbl 0577.58032
-[1] On manifolds of negative curvature with isospectral potentials, Topology, 26 (1987), 63-66. | MR 880508 | Zbl 0617.53048
-[2] Constructing isospectral manifolds, Amer. Math. Monthly, 95 (1988), 823-839. | MR 967343 | Zbl 0673.58046
-[3] Isospectral potentials on a surface of genus 3, Math. Sciences Reach. Institute series, Ed. D. Drasin, "Holomorphic functions and moduli", Springer, 1988, 203-208. | MR 955822 | Zbl 0657.58047
-[1] Isospectral sets of conformally equivalent metrics, Duke Math. J., à paraître. | Zbl 0667.53037
, , -[1] Isospectral surfaces of small genus, Nagoya Math. J., 107 (1987), 13-24. | MR 909246 | Zbl 0605.58041
, -[1] Can one hear the dimension of a fractal, Comm. Math. Phys., 104 (1986), 103-122. | MR 834484 | Zbl 0607.58043
, -[1] On the compactness of isospectral potentials, Comm. Partial Diff. Eq., 9 (1984), 687-698. | MR 745021 | Zbl 0547.58039
-[1] Spektrale Starrheit gewisser Drehflächen, Math. Ann., 269 (1984), 95-101. | MR 756778 | Zbl 0553.53028
, -[1] Isospectral Riemann surfaces, Ann. Inst. Fourier, 36 (1986), 167- 192. | Numdam | MR 850750 | Zbl 0579.53036
-[2] Riemannsche Flächen und Längenspektrum vom Trigonometrischen Standpunkte aus, Habilitationsschrift, Bonn, 1980.
-[3] Sur le spectre de longueurs des surfaces de Riemann, C. R. Acad. Sci. Paris Sér. I Math., 292 (1981), 487-498. | MR 612543 | Zbl 0466.32012
-[4] Cayley graphs and planar isospectral domains, Proc. Taniguchi Symp. "Geometry and Analysis on manifolds" 1987, Lecture Notes in Math. Springer , 1339 (1988), 64-77. | MR 961473 | Zbl 0647.53034
-[5] Geometry and spectrum of compact Riemann surfaces, livre en préparation. | Zbl 0770.53001
-[1] Finite parts of the spectrum of a Riemann surface, Prépublication de l'Institut Fourier n° 121, Grenoble , 1989. | MR 1060691
, -[1] The geometry and spectrum of the one holed torus, Comment. Math. Helv., 63 (1988), 259-274. | MR 948781 | Zbl 0649.53028
, -[1]
- PhD Thesis, University of Pennsylvania, 1988.[1] On hearing the shape of a triangle, Proc. Amer. Math. Soc., à paraître. | Zbl 0721.58053
, -[1] Compactness of isospectral conformal metrics on S3, Comment. Math. Helv., à paraître. | Zbl 0679.53038
, -[2] The conformal deformation equation and isospectral sets of conformal metrics, Preprint, U. Southem Cal., 1988. | MR 925123
, -[3] A compactness theorem for conformal metrics on -manifolds and application to isospectral metrics, Preprint, U. Southern Cal., 1988.
, -[1] Eigenvalues in Riemannian geometry, Acad. Press, 1984. | MR 768584 | Zbl 0551.53001
-[1] On the construction of isospectral but non isometric Riemannian manifolds, Preprint, 1988 Louisiana State University Baton Rouge.
. -[1] Introducere în Geometria Spectrală, Editions République Socialiste Roumaine, Bucarest, 1988. | MR 1011669
, -[1] Audible and inaudible geometric properties, Preprint U. Pennsylvania, 1988. | MR 1122855
-[1] Isospectral deformations I : Riemannian structures on two-step nilspaces, Comm. Pure Appl. Math., 40 (1987), 367-387. | MR 882070 | Zbl 0649.53025
, -[2] Isospectral metrics and finite Riemannian coverings, Contemporary Mathematics, Amer. Math. Soc., 64 (1987), 79-92. | MR 881457 | Zbl 0646.58030
, -[3] Isospectral Riemannian metrics and potentials, Proc. Amer. Math. Soc., 17 (1987), 137-139. | MR 888890 | Zbl 0629.58008
, -[4] Isospectral Riemannian metrics and potentials, Preprint Univ. Pennsylvania, 1987. | MR 888890
, -[1] You cannot hear the size of a homology class, Comment. Math. Helv., à paraître.
, , , -[1]
- PhD Thesis, M.I.T., 1988.[1] A construction of nonflat, compact irreducible Riemannian manifolds which are isospectral but not isometric, Math. Z., 168 (1979), 207-212. | MR 544590 | Zbl 0396.53022
-[1] Analytic torsion and Prym differentials, Ann. of Math. Stud., 97 (1981), 107-122. | MR 624809 | Zbl 0458.30025
-[1] Tambour fractal : vers une résolution de la conjecture de Weyl-Berry pour les valeurs propes du laplacien, C. R. Acad. Sci. Paris Sér. I Math., 306 (1988), 171. | MR 930556 | Zbl 0654.35079
, -[1] Invariance theory for the heat equation and the Atiyah-Singer index theorem, Publish or Perish Inc., 1984. | MR 783634 | Zbl 0565.58035
-[2] On spherical space-forms with meta-cyclic fundamental group which are isospectral but not equivariant cobordant, Compositio Math., 56 (1985), 171-200. | Numdam | MR 809865 | Zbl 0593.58041
-[3] Leading terms in the asymptotics of the heat equation, Contemporary Math., 73 (1988), 79-85. | MR 954631 | Zbl 0661.58034
-[1] Riemannian manifolds isospectral on functions but not on 1- forms, J. Diff. Geom., 24 (1986), 79-96. | MR 857377 | Zbl 0585.53036
-[2] The Laplace spectrum versus the length spectra of Riemannian manifolds, in Nonlinear Problems in Geometry (D.M. De Turck, ed.) Contemporary Math., 51 (1986), 63-80. | MR 848934 | Zbl 0591.53042
-[1] Isospectral deformations of compact solvmanifolds, J. Diff. Geom., 19 (1984), 241-256. | MR 739790 | Zbl 0523.58043
, -[2] The spectrum of the Laplacian on Riemannian Heisenberg manifolds, Michigan Math. J., 33 (1986), 253-271. | MR 837583 | Zbl 0599.53038
, -[3] Isometry groups of Riemannian solvmanifolds, Trans. Amer. Math. Soc., 307 (1988), 245-269. | MR 936815 | Zbl 0664.53022
, -[1] Lectures on spectral theory of elliptic operators, Duke Math. J., 44 (1977), 485-517. | MR 448452 | Zbl 0463.58024
-[2] Inverse spectral problems in geometry, Preprint M.I.T., 1988.
-[1] Some inverse spectral results for negatively curved 2-manifolds, Topology, 19 (1980), 153-180. | MR 579579 | Zbl 0456.58031
, -[2] Some inverse spectral results for negatively curved n-manifolds, Proc. Symp. Pure Math., Geometry of the Laplace Operator, Amer. Math. Soc., 36 (1980), 153-180. | MR 573432 | Zbl 0456.58031
, -[1] Subgroups inducing the same permutation representation, J. of Algebra, 81 (1983), 312-319. | MR 700287 | Zbl 0527.20005
-[1] Length spectra as moduli for hyperbolic surfaces, Duke Math. J., 5 (1985), 922-935. | MR 816393 | Zbl 0595.30052
-[1] The Selberg trace formula and the Riemann zeta function, Duke Math. J., 43 (1976), 441-482. | MR 414490 | Zbl 0346.10010
-[2] The Selberg trace formula for PSL(2, R), Vol. I : Lecture Notes in Math. Springer 548, 1976 Vol. II : Lecture Notes in Math. Springer 1001, 1983. | MR 439755 | Zbl 0347.10018
-[1] Isospectral problem for spherical space forms, in spectra of Riemannian Manifolds, ed. by M. Berger, S. Murakami and T. Ochiai, Kaigai Publications (1983), 57-63.
-[2] Riemannian manifolds p-isospectral but not (p + 1)-isospectral, Preprint Hiroshima University, 1989. | MR 1040537
-[1] Can one hear the shape of a drum ?, Amer. Math. Monthly, 73 (1966), 1-23. | MR 201237 | Zbl 0139.05603
-[1] Collars on Riemann surfaces, Princeton U. Press, Ann. of Math. Stud., 79 (1974), 263-268. | MR 379833 | Zbl 0304.30014
-[1] Positive definite quadratic forms with the same representation numbers, Arch. Math., 28 (1977), 495-497. | MR 441864 | Zbl 0361.10019
-[1] Lineare Relationen zwischen Darstellungszahlen quadratischer Formen, Math. Ann., 168 (1967), 31-39. | MR 205943 | Zbl 0146.05901
-[1] On isospectral deformations of Riemannian metrics, Compositio Math., 40 (1980), 319-324. | Numdam | MR 571054 | Zbl 0406.53038
-[2] On the characterization of flat metrics by the spectrum, Comment. Math. Helv., 55 (1980), 427-444. | MR 593057 | Zbl 0448.58027
-[3] On isospectral deformations of Riemannian metrics II, Compositio Math., 47 (1982), 195-205. | Numdam | MR 677020 | Zbl 0505.53019
-[1] Selberg's trace formula as applied to a compact Riemann surface, Comm. Pure Appl. Math., 25 (1972), 225-246. | MR 473166
-[2] Curvature and the eigenvalues of the Laplacian, J. Differential Geom., 1 (1967), 43-69. | MR 217739 | Zbl 0198.44301
, -[1] Isospectral sets of drumheads are compact in C∞, Preprint M.S.R.I. Berkeley, 1984.
-[1] Eigenvalues of the Laplace operator on certain manifolds, Proc. Nat. Acad. Sci., 51 (1964), 542. | MR 162204 | Zbl 0124.31202
-[1] Spectral rigidity for manifolds with negative curvature operator, Contemp. Math. Nonlinear Problems in Geometry, 51 (1986), 99-103. | MR 848937 | Zbl 0591.53041
-[1] A remark on Mahler's compactness theorem, Proc. Amer. Math. Soc., 28 (1971), 289-294. | MR 276410 | Zbl 0215.23202
-[1] On the positivity of the effective action in a theory of random surfaces, Comm. Math. Phys., 86 (1982), 321-326. | MR 677001 | Zbl 0506.47031
-[1] Extremals of determinants of Laplacians, J. Funct. Anal., 80 (1988), 148-211. | MR 960228 | Zbl 0653.53022
, , -[2] Compact isospectral sets of Riemann surfaces, J. Funct. Anal., 80 (1988), 212-234. | MR 960229 | Zbl 0653.53021
, , -[3] Compact isospectral sets of plane domains, Proc. Nat. Acad. Sci. U.S.A., 85 (1988), 5359-5361. | MR 952815 | Zbl 0674.30021
, , -[4] Moduli space, heights and isospectral sets of plane domains, Ann. of Math., à paraître. | Zbl 0677.58045
, , -[1] Le spectre marqué des longueurs des surfaces à courbure négative, Preprint Orsay, 1988. | MR 1038361
-[1] Curvature and the fundamental solution of the heat equation, J. Indian Math. Soc., 34 (1970), 269-285. | MR 488181 | Zbl 0237.53039
-[1] On the equation ζK(s) = ζK'(s), J. Number Theory, 9 (1977), 342-360. | Zbl 0389.12006
-[1] Determinants of Laplacians; heights and finiteness, Preprint Stanford U., 1988. | MR 1039364
-[1] Exotic structures on 4-manifolds detected by spectral invariants, Invent. Math., 94 (1988), 147-162. | MR 958593 | Zbl 0656.58032
-[1] Spectrum of a compact flat manifold, Comment. Math. Helv., 53 (1978), 613-621. | MR 511851 | Zbl 0422.53023
-[2] Fundamental groups and Laplacians, Proc. Taniguchi Symp. "Geometry and Analysis on Manifolds" 1987, Lecture Notes in Math. Springer , 1339 (1988), 248-277. | MR 961485 | Zbl 0646.58027
-[3] Riemannian coverings and isospectral manifolds, Ann. of Math., 121 (1985), 169-186. | MR 782558 | Zbl 0585.58047
-[1] A lower bound for the number of isospectral surfaces of arbitrarily large genus, PhD Thesis U. Southern Cal., 1988. | MR 1034979
-[1] Bounded domains which are isospectral but not congruent, Ann. Sci. Ecole Norm. Sup., 15 (1982), 441-456. | Numdam | MR 690649 | Zbl 0505.58036
-[1] Some remarks on the problem of isospectrality, Preprint Princeton, 1988.
-[1] Exemples de sous-groupes discrets non conjugués de PSL(2, R) qui ont même fonction zêta de Selberg, C.R. Acad. Sci. Paris, 287 (1978), 47-49. | MR 491604 | Zbl 0387.10013
-[2] Variétés riemanniennes isospectrales et non isométriques, Ann. of Math., 112 (1980), 21-32. | MR 584073 | Zbl 0445.53026
-[1] Eine Identität zwischen Modulformen zweiten Grades, Abh. Sem. Univ. Hamburg, 14 (1941), 289-322. | JFM 67.0296.01 | MR 5508 | Zbl 0025.01701
-[1] The eigenvalue spectrum as moduli for compact Riemann surfaces, Bull. Amer. Math. Soc., 83 (1977), 1306-1308. | MR 499329 | Zbl 0368.32009
-[2] The Eigenvalue Spectrum as Moduli for Flat Tori, Trans. Amer. Math. Soc., 244 (1978), 313-321. | MR 514879 | Zbl 0405.58051
-[3] The length spectrum as moduli for compact Riemann surfaces, Ann. Math., 109 (1979), 323-351. | MR 528966 | Zbl 0441.30055
-[4] Asymptotics of the spectrum and the Selberg zêta function on the space of Riemann surfaces, Comm. Math. Phys., 112 (1987), 283-315. | MR 905169 | Zbl 0629.58029
-