Voir la notice du chapitre de livre provenant de la source Numdam
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://geodesic.mathdoc.fr/item/SB_1988-1989__31__127_0/
@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},
series = {Ast\'erisque},
note = {talk:705},
pages = {127--154},
year = {1989},
publisher = {Soci\'et\'e math\'ematique de France},
number = {177-178},
mrnumber = {1040571},
zbl = {0703.53035},
language = {fr},
url = {http://geodesic.mathdoc.fr/item/SB_1988-1989__31__127_0/}
}
TY - CHAP AU - Bérard, Pierre TI - Variétés riemanniennes isospectrales non isométriques BT - Séminaire Bourbaki : volume 1988/89, exposés 700-714 AU - Collectif T3 - Astérisque N1 - talk:705 PY - 1989 SP - 127 EP - 154 IS - 177-178 PB - Société mathématique de France UR - http://geodesic.mathdoc.fr/item/SB_1988-1989__31__127_0/ LA - fr ID - SB_1988-1989__31__127_0 ER -
%0 Book Section %A Bérard, Pierre %T Variétés riemanniennes isospectrales non isométriques %B Séminaire Bourbaki : volume 1988/89, exposés 700-714 %A Collectif %S Astérisque %Z talk:705 %D 1989 %P 127-154 %N 177-178 %I Société mathématique de France %U http://geodesic.mathdoc.fr/item/SB_1988-1989__31__127_0/ %G fr %F 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. | Zbl | MR
[1] , , - Le spectre d'une variété riemannienne, Lecture Notes in Math. Springer 194, 1971. | Zbl | MR
[1] - Tores isospectraux en dimension 3, C. R. Acad. Sci. Paris Sér. I Math., 292 (1981), 163-166. | Zbl | MR
[1] - Determination of a Riemannian metric form the first variation of its spectrum, Amer. J. Math., 107 (1985), 815-831. | Zbl | MR
[1] - On manifolds of negative curvature with isospectral potentials, Topology, 26 (1987), 63-66. | Zbl | MR
[2] - Constructing isospectral manifolds, Amer. Math. Monthly, 95 (1988), 823-839. | Zbl | MR
[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. | Zbl | MR
[1] , , - Isospectral sets of conformally equivalent metrics, Duke Math. J., à paraître. | Zbl
[1] , - Isospectral surfaces of small genus, Nagoya Math. J., 107 (1987), 13-24. | Zbl | MR
[1] , - Can one hear the dimension of a fractal, Comm. Math. Phys., 104 (1986), 103-122. | Zbl | MR
[1] - On the compactness of isospectral potentials, Comm. Partial Diff. Eq., 9 (1984), 687-698. | Zbl | MR
[1] , - Spektrale Starrheit gewisser Drehflächen, Math. Ann., 269 (1984), 95-101. | Zbl | MR
[1] - Isospectral Riemann surfaces, Ann. Inst. Fourier, 36 (1986), 167- 192. | Zbl | MR | Numdam
[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. | Zbl | MR
[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. | Zbl | MR
[5] - Geometry and spectrum of compact Riemann surfaces, livre en préparation. | Zbl
[1] , - Finite parts of the spectrum of a Riemann surface, Prépublication de l'Institut Fourier n° 121, Grenoble , 1989. | MR
[1] , - The geometry and spectrum of the one holed torus, Comment. Math. Helv., 63 (1988), 259-274. | Zbl | MR
[1] - PhD Thesis, University of Pennsylvania, 1988.
[1] , - On hearing the shape of a triangle, Proc. Amer. Math. Soc., à paraître. | Zbl
[1] , - Compactness of isospectral conformal metrics on S3, Comment. Math. Helv., à paraître. | Zbl
[2] , - The conformal deformation equation and isospectral sets of conformal metrics, Preprint, U. Southem Cal., 1988. | MR
[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. | Zbl | MR
[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
[1] - Audible and inaudible geometric properties, Preprint U. Pennsylvania, 1988. | MR
[1] , - Isospectral deformations I : Riemannian structures on two-step nilspaces, Comm. Pure Appl. Math., 40 (1987), 367-387. | Zbl | MR
[2] , - Isospectral metrics and finite Riemannian coverings, Contemporary Mathematics, Amer. Math. Soc., 64 (1987), 79-92. | Zbl | MR
[3] , - Isospectral Riemannian metrics and potentials, Proc. Amer. Math. Soc., 17 (1987), 137-139. | Zbl | MR
[4] , - Isospectral Riemannian metrics and potentials, Preprint Univ. Pennsylvania, 1987. | MR
[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. | Zbl | MR
[1] - Analytic torsion and Prym differentials, Ann. of Math. Stud., 97 (1981), 107-122. | Zbl | MR
[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. | Zbl | MR
[1] - Invariance theory for the heat equation and the Atiyah-Singer index theorem, Publish or Perish Inc., 1984. | Zbl | MR
[2] - On spherical space-forms with meta-cyclic fundamental group which are isospectral but not equivariant cobordant, Compositio Math., 56 (1985), 171-200. | Zbl | MR | Numdam
[3] - Leading terms in the asymptotics of the heat equation, Contemporary Math., 73 (1988), 79-85. | Zbl | MR
[1] - Riemannian manifolds isospectral on functions but not on 1- forms, J. Diff. Geom., 24 (1986), 79-96. | Zbl | MR
[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. | Zbl | MR
[1] , - Isospectral deformations of compact solvmanifolds, J. Diff. Geom., 19 (1984), 241-256. | Zbl | MR
[2] , - The spectrum of the Laplacian on Riemannian Heisenberg manifolds, Michigan Math. J., 33 (1986), 253-271. | Zbl | MR
[3] , - Isometry groups of Riemannian solvmanifolds, Trans. Amer. Math. Soc., 307 (1988), 245-269. | Zbl | MR
[1] - Lectures on spectral theory of elliptic operators, Duke Math. J., 44 (1977), 485-517. | Zbl | MR
[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. | Zbl | MR
[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. | Zbl | MR
[1] - Subgroups inducing the same permutation representation, J. of Algebra, 81 (1983), 312-319. | Zbl | MR
[1] - Length spectra as moduli for hyperbolic surfaces, Duke Math. J., 5 (1985), 922-935. | Zbl | MR
[1] - The Selberg trace formula and the Riemann zeta function, Duke Math. J., 43 (1976), 441-482. | Zbl | MR
[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. | Zbl | MR
[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
[1] - Can one hear the shape of a drum ?, Amer. Math. Monthly, 73 (1966), 1-23. | Zbl | MR
[1] - Collars on Riemann surfaces, Princeton U. Press, Ann. of Math. Stud., 79 (1974), 263-268. | Zbl | MR
[1] - Positive definite quadratic forms with the same representation numbers, Arch. Math., 28 (1977), 495-497. | Zbl | MR
[1] - Lineare Relationen zwischen Darstellungszahlen quadratischer Formen, Math. Ann., 168 (1967), 31-39. | Zbl | MR
[1] - On isospectral deformations of Riemannian metrics, Compositio Math., 40 (1980), 319-324. | Zbl | MR | Numdam
[2] - On the characterization of flat metrics by the spectrum, Comment. Math. Helv., 55 (1980), 427-444. | Zbl | MR
[3] - On isospectral deformations of Riemannian metrics II, Compositio Math., 47 (1982), 195-205. | Zbl | MR | Numdam
[1] - Selberg's trace formula as applied to a compact Riemann surface, Comm. Pure Appl. Math., 25 (1972), 225-246. | MR
[2] , - Curvature and the eigenvalues of the Laplacian, J. Differential Geom., 1 (1967), 43-69. | Zbl | MR
[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. | Zbl | MR
[1] - Spectral rigidity for manifolds with negative curvature operator, Contemp. Math. Nonlinear Problems in Geometry, 51 (1986), 99-103. | Zbl | MR
[1] - A remark on Mahler's compactness theorem, Proc. Amer. Math. Soc., 28 (1971), 289-294. | Zbl | MR
[1] - On the positivity of the effective action in a theory of random surfaces, Comm. Math. Phys., 86 (1982), 321-326. | Zbl | MR
[1] , , - Extremals of determinants of Laplacians, J. Funct. Anal., 80 (1988), 148-211. | Zbl | MR
[2] , , - Compact isospectral sets of Riemann surfaces, J. Funct. Anal., 80 (1988), 212-234. | Zbl | MR
[3] , , - Compact isospectral sets of plane domains, Proc. Nat. Acad. Sci. U.S.A., 85 (1988), 5359-5361. | Zbl | MR
[4] , , - Moduli space, heights and isospectral sets of plane domains, Ann. of Math., à paraître. | Zbl
[1] - Le spectre marqué des longueurs des surfaces à courbure négative, Preprint Orsay, 1988. | MR
[1] - Curvature and the fundamental solution of the heat equation, J. Indian Math. Soc., 34 (1970), 269-285. | Zbl | MR
[1] - On the equation ζK(s) = ζK'(s), J. Number Theory, 9 (1977), 342-360. | Zbl
[1] - Determinants of Laplacians; heights and finiteness, Preprint Stanford U., 1988. | MR
[1] - Exotic structures on 4-manifolds detected by spectral invariants, Invent. Math., 94 (1988), 147-162. | Zbl | MR
[1] - Spectrum of a compact flat manifold, Comment. Math. Helv., 53 (1978), 613-621. | Zbl | MR
[2] - Fundamental groups and Laplacians, Proc. Taniguchi Symp. "Geometry and Analysis on Manifolds" 1987, Lecture Notes in Math. Springer , 1339 (1988), 248-277. | Zbl | MR
[3] - Riemannian coverings and isospectral manifolds, Ann. of Math., 121 (1985), 169-186. | Zbl | MR
[1] - A lower bound for the number of isospectral surfaces of arbitrarily large genus, PhD Thesis U. Southern Cal., 1988. | MR
[1] - Bounded domains which are isospectral but not congruent, Ann. Sci. Ecole Norm. Sup., 15 (1982), 441-456. | Zbl | MR | Numdam
[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. | Zbl | MR
[2] - Variétés riemanniennes isospectrales et non isométriques, Ann. of Math., 112 (1980), 21-32. | Zbl | MR
[1] - Eine Identität zwischen Modulformen zweiten Grades, Abh. Sem. Univ. Hamburg, 14 (1941), 289-322. | Zbl | MR | JFM
[1] - The eigenvalue spectrum as moduli for compact Riemann surfaces, Bull. Amer. Math. Soc., 83 (1977), 1306-1308. | Zbl | MR
[2] - The Eigenvalue Spectrum as Moduli for Flat Tori, Trans. Amer. Math. Soc., 244 (1978), 313-321. | Zbl | MR
[3] - The length spectrum as moduli for compact Riemann surfaces, Ann. Math., 109 (1979), 323-351. | Zbl | MR
[4] - Asymptotics of the spectrum and the Selberg zêta function on the space of Riemann surfaces, Comm. Math. Phys., 112 (1987), 283-315. | Zbl | MR