Inégalités isopérimétriques et applications
Bérard, Pierre ; Meyer, Daniel
Annales scientifiques de l'École Normale Supérieure, Tome 15 (1982), p. 513-541 / Harvested from Numdam
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     author = {B\'erard, Pierre and Meyer, Daniel},
     title = {In\'egalit\'es isop\'erim\'etriques et applications},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {15},
     year = {1982},
     pages = {513-541},
     doi = {10.24033/asens.1435},
     mrnumber = {84h:58147},
     zbl = {0527.35020},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_1982_4_15_3_513_0}
}

Bérard, Pierre; Meyer, Daniel. Inégalités isopérimétriques et applications. Annales scientifiques de l'École Normale Supérieure, Tome 15 (1982) pp. 513-541. doi : 10.24033/asens.1435. http://gdmltest.u-ga.fr/item/ASENS_1982_4_15_3_513_0/

[AN] T. Aubin, Problèmes isopérimétriques et espaces de Sobolev (J. Differential Geometry, vol. 11, 1976, p. 573-598). | MR 56 #6711 | Zbl 0371.46011

[AR] N. Aronsajn, A Unique Continuation Theorem for Solutions of Elliptic Partial Differential Equations or Inequalities of Second Order (J. Math. Pures et Appliquées, vol. 36, 1957, p. 235-249). | MR 19,1056c | Zbl 0084.30402

[B-B] L. Bérard Bergery et J. P. Bourguignon, Laplacians and Riemannian Submersions with Totally Geodesic Fibres, prétirage, Ecole Polytechnique, Palaiseau, France, 1980.

[B-C] R. Bishop et R. Crittenden, Geometry of Manifolds, Academic Press, 1964, New York. | MR 29 #6401 | Zbl 0132.16003

[B-D] J. L. Barbosa et M. Do Carmo, A Proof of a General Isoperimetric Inequality for Surfaces (Math. Z., vol. 162, 1978, p. 245-261). | MR 80f:53043 | Zbl 0369.53054

[BE] C. Bandle, Isoperimetric Inequalities and Applications (Monographs and Studies in Math., n° 7, Pitman, 1980). | MR 81e:35095 | Zbl 0436.35063

[BG] J. Brüning, Ueber Knoten von Eigenfunktionen des Laplace-Beltrami Operators (Math. Z., vol. 158, 1978, p. 15-21). | Zbl 0349.58012

[B-G-M] M. Berger, P. Gauduchon et E. Mazet, Le spectre d'une variété riemannienne, (Lecture Notes in Math., n° 194, Springer, 1971). | MR 43 #8025 | Zbl 0223.53034

[B-J-S] L. Bers, F. John et M. Schechter, Partial Differential Équations, Interscience, 1964, New York. | MR 29 #346 | Zbl 0126.00207

[B-K] D. Barthel et R. Kümritz, Laplacian with a Potential, in Global Differential Geometry and Global Analysis, Proceedings, Berlin, 1979, (Lecture Note in Math., n° 838, Springer, 1981). | Zbl 0437.53033

[B-M] P. Bérard et D. Meyer, Une généralisation de l'inégalité de Faber-Krahn (C. R. Acad. Sc. Paris, t. 292, 1981, p. 437). | MR 82j:58107 | Zbl 0462.53026

[BN] G. Besson, Sur la multiplicité de la première valeur propre des surfaces riemanniennes, (Ann. Institut Fourier, vol. 30, 1980, p. 109-128). | Numdam | MR 81h:58059 | Zbl 0417.30033

[CG] S.-Y. Cheng, Eigenfunctions and Nodal Sets (Comment. Math. Helv., vol. 51, 1976, p. 43-55). | MR 53 #1661 | Zbl 0334.35022

[C-H] R. Courant et D. Hilbert, Methods of Mathematical Physics, vol. I, Interscience, 1953. | MR 16,426a | Zbl 0051.28802

[C-N] I. Chavel et E. A. Feldman, Spectra of Domains in Compact Manifolds (J. Functional Analysis, vol. 30, 1978, p. 198-222). | MR 80c:58027 | Zbl 0392.58016

[CV] Y. Colin De Verdière, communication privée.

[D-G] J. Duistermaat et V. Guillemin, The Spectrum of Positive Elliptic Operators and Periodic Bicharacteristics (Inventiones Math., vol. 29, 1975, p. 39-79). | MR 53 #9307 | Zbl 0307.35071

[F-H] S. Friedland et W. K. Hayman, Eigenvalues Inequalities for the Dirichlet Problem on Spheres and Growth of Subharmonic Functions (Comment. Math. Helv., vol. 51, 1976, p. 133-161). | MR 54 #568 | Zbl 0339.31003

[FR] G. Faber, Beweis dass unter allen Homogenen Membranen von Gleicher Fläche und Gleicher Spannung die Kreisförmige den Tiefsten Grundton Gibt (S.-B. Math. Nat. Kl. Bayer Akad. Wiss., 1923, p. 169-172). | JFM 49.0342.03

[GA] S. Gallot, Minorations sur le λ1 des variétés riemanniennes (Séminaire Bourbaki, 1980/1981, exposé n° 569). | Numdam | Zbl 0493.53034

[G-M] A. Gray et G. B. Mathews, A Treatise on Bessel Functions and their Applications to Physics, Dover, 1966. | Zbl 0135.28002

[G-T] D. Gilbarg et N. S. Trudinger, Elliptic Partial Differential Equations of Second Order (Grundlehren der Math., vol. 224, Springer, 1977). | MR 57 #13109 | Zbl 0361.35003

[GV] M. Gromov, Paul Levy's Isoperimetric Inequality, prétirage I.H.E.S., 1980.

[KN] E. Krahn, Über eine von Rayleigh Formulierte Minimaleigenschaft der Kreise (Math. Ann., vol. 94, 1924, p. 97-100). | JFM 51.0356.05

[KZ] J. Kazdan, communication privée.

[LY] H. Lewy, On the Minimum Number of Domains in which the Nodal Lines of Spherical Harmonics Divide the Sphere (Comm. in Partial Differential Equations, vol. 2, 1977, p. 1233-1244). | MR 57 #16740 | Zbl 0377.31008

[PE] J. Peetre, A generalization of Courant's Nodal Domain Theorem (Math. Scand., vol. 5, 1957, p. 15-20). | MR 19,1180a | Zbl 0077.30101

[PL] A. Pleijel, Remarks on Courant's Nodal Line Theorem (Comm. on Pure Applied Math., vol. 9, 1956, p. 543-550). | MR 18,315d | Zbl 0070.32604

[P-S] G. Polya et G. Szegö, Isoperimetric Inequalities in Mathematical Physics (Annals of Math. Studies, n° 27, Princeton, 1951). | MR 13,270d | Zbl 0044.38301

[RY] R. C. Reilly, Applications of the Hessian Operator in a Riemannian Manifold (Indiana University Math. J., vol. 26, 1977, p. 459-472). | MR 57 #13799 | Zbl 0391.53019

[SR] E. Sperner, Zur Symmetrisierung von Funktionen auf Sphären (Math. Z., vol. 134, 1973, p. 317-327). | MR 49 #5310 | Zbl 0283.26015

[ST] E. Schmidt, Der Brunn-Minkowskische Satz und sein Spiegeltheorem sowie die isoperimetrische Eigenschaft der Kugel in der euklidischen und nichteuklidischen Geometrie (Math. Nachrichten, vol. 2, 1949, p. 171-244). | MR 11,534l | Zbl 0041.51001

[UK] K. Uhlenbeck, Generic Properties of Eigenfunctions (Amer. J. Math., vol. 98, 1976, p. 1059-1078). | MR 57 #4264 | Zbl 0355.58017

[WN] G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd éd., Cambridge, 1944. | MR 6,64a | Zbl 0174.36202

[W-W] E. T. Whittaker et G. N. Watson, A Course on Modern Analysis, 4th éd., Cambridge, 1969.