Inégalités isopérimétriques et analytiques sur les variétés riemanniennes

On the Geometry of Differentiable Manifolds Rome, 23-27 juin 1986, Astérisque no. 163-164 (1988), p. 31-91

@incollection{AST_1988__163-164__31_0,
     author = {Gallot, Sylvestre},
     title = {In\'egalit\'es isop\'erim\'etriques et analytiques sur les vari\'et\'es riemanniennes},
     booktitle = {On the Geometry of Differentiable Manifolds Rome, 23-27 juin 1986},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {163-164},
     year = {1988},
     pages = {31-91},
     zbl = {0674.53001},
     language = {fr},
     url = {http://www.numdam.org/item/AST_1988__163-164__31_0}
}

Gallot, Sylvestre. Inégalités isopérimétriques et analytiques sur les variétés riemanniennes, in On the Geometry of Differentiable Manifolds Rome, 23-27 juin 1986, Astérisque, no. 163-164 (1988), pp. 31-91. http://www.numdam.org/item/AST_1988__163-164__31_0/

References

[AN] Almgren F. — Existence and regularity almost everywhere of solutions to elliptic variational problems, Mem. Am. Math. Soc. 165 (vol. 4), 1976. | Zbl 0327.49043

[A-S] Abramowitz M., Stegun I. — Handbook Of Mathematical Functions, Dover, 1965.

[AT] Azencott R.— Behaviour of diffusion semi-groups at infinity, Bull. Soc. Math, France , 102 (1974), 193-240. | Article | Zbl 0293.60071

[AU] Aubin T. — Problèmes isopérimétriques et espaces de Sobolev, J. Differential Geom., 11 (1976), 573-598. | Article | Zbl 0371.46011

[BA] Bandle C. — Isoperimetric inequalities and applications, Monographs and Studies in Maths, Pitman, 1980. | Zbl 0519.53037

[B-B-G] Bérard P. , Besson G., Gallot S. — Sur une inégalité isopérimétrique qui généralise celle de Paul Lévy-Gromov, Invent. Math., 80 (1985), 295-308. | Article | Zbl 0571.53027

[B-C] Bishop R., Crittenden R. — Geometry of Manifolds, Acad. Press, New-York, 1964. | Zbl 0132.16003

[BE1] Bérard P. — Spectres et groupes cristallographiques I, Domaines Euclidiens, Invent. Math., 58 (1980), 179-199. | Article | Zbl 0434.35068

[BE2] Bérard P. — Spectral Geometry : Direct and Inverse Problems, Lecture Notes in Math. Springer 1207, 1986. | Zbl 0608.58001

[B-G1] Bérard P., Gallot S.— Inégalités isopérimétriques pour l'équation de la chaleur et application à l'estimation de quelques invariants, Séminaire Goulaouic-Meyer-Schwartz, exposé XV, Ecole Polytechnique Palaiseau, 1984. | Zbl 0542.53025

[B-G2] Bérard P. , Gallot S. — Notes d'un cours à l'Ec. Norm. Sup. Paris (non publié), 1985.

[B-G-M] Berger M., Gauduchon P. , Mazet E. — Le spectre d'une variété riemannienne, Lecture Notes in Math. Springer 194, 1971. | Zbl 0223.53034

[BI] Bombieri E. — Theory of minimal surfaces and a counter-example to Bernstein conjecture in High Dimension, Lecture Notes, Courant Institut, 1970.

[B-M] Bérard P., Meyer D. — Inégalités isopérimétriques et applications, Ann. Sci. École Norm. Sup., 15 (1982), 513-542. | Article | Zbl 0527.35020

[B-P] Bavard C., Pansu P. — Sur le volume minimal de $ℝ^{2}$ , Ann. Sci.Ecole Norm. Sup., 19 (1986), 479-490. | Article | Zbl 0611.53038

[BR] Berger M. — Cours à l'Université d'Osaka (rédigé par T. Tsujishita), Public, of the Department of Math, of Osaka University, Toyonaka (in Japanese), nov.1981.

[BU1] Buser P.—A note on the isoperimetric constant, Ann. Sci. École Norm. Sup., 15 (1982), 213-230. | Article | Zbl 0501.53030

[BU2] Buser P.— On Cheeger's Inequality $λ_{1} ⩾ h^{2} / 4$ , in Geometry of the Laplace Operator, Proc. Symposia in Pure Math, 36 (1980), 29-77. | Zbl 0432.58024

[CH] Cheng S. Y.— Eigenvalue comparison theorems and its geometric applications, Math. Z, 143 (1975), 289- 297. | Article | Zbl 0329.53035

[CHE] Cheeger J. —A lower bound for the smallest eigenvalue of the Laplacian, Problems in Analysis, A Symposium in Honor of Salomon Bochner, Robert C. Gunning editor, Princeton Univ. Press 195-199, 1970. | Zbl 0212.44903

[C-G] Colin De Verdière Y., Gallot S. — non publié,.

[CL] Chavel I.— Eigenvalues in Riemannian Geometry, Pure Appl. Math., 1984. | Zbl 0551.53001

[CR1] Croke C. B.— Some isoperimetric inequalities and eigenvalues estimates, Ann. Sci. École Norm. Sup., 13 (1980), 419-435. | Article | Zbl 0465.53032

[CR2] Croke C. B. — An eigenvalues pinching theorem, Invent Math., 68 (1982), 253-256. | Article | Zbl 0505.53018

[CR-GV]

Cheeger J., Gromov M. — Collapsing Riemannian Manifolds while keeping their curvature bounded, preprint. | Article | Zbl 0606.53028

[DK] Dodziuk J. — Maximum Principle For Parabolic Inequalities And The Heat Flow On Open Manifolds, Indiana Univ. Math. J, 32 (1983), 703-716. | Article | Zbl 0526.58047

[FA1] Fukaya K.— Collapsing Riemannian manifolds and eigenvalues of the Laplace operator, Inv. Math., 87 (1987), 517-547. | Article | Zbl 0589.58034

[FA2] Fukaya K.—A boundary of the set of Riemannian manifolds with bounded curvature and diameter, Preprint, 1986. | Zbl 0652.53031

[FR] Faber G. — Beweis dassunter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundtongibt, Sitzungsber. Bayer. Akad. der Wiss. Math.-Phys., Munich, 169-172, 1923. | JFM 49.0342.03

[FS] Friedrichs K. O.—Differential Forms On Riemannian Manifolds, Comm. in pure and applied Math, vol. VIII (1955), 551-590. | Article | Zbl 0066.07504

[GE] Gage M.— Upper Bounds for the First Eigenvalue of the Laplace-Beltrami Operator, Indiana Univ. Math. J., 29 (1980), 897-912. | Article | Zbl 0465.53031

[G-H-L] Gallot S., Hulin D., Lafontaine J. — Riemannian Geometry, Universitext, Springer, 1987. | Zbl 1068.53001

[G-M] Gallot S., Meyer D.— D'un résultat hilbertien à un principe de comparaison entre spectres. Applications, Prépublication Institut Fourier, n° 82, Grenoble, 1987. | Zbl 0722.53037

[GT1] Gallot S. — Variétés dont le spectre ressemble à celui d'une sphère, Astérisque , 80, 1980. | Zbl 0471.53027

[GT2] Gallot S. — Inégalités isopérimétriques sur les variétés compactes sans bord, Preprint Univ. Savoie, exposé par M. Berger dans [BR], Juin 1981.

[GT3] Gallot S. — A Sobolev inequality and some geometric applications, Spectra of Riemannian Manifolds (actes du colloque de Kyoto 1981), Kaigai Publ., 45-55, 1983.

[GT4] Gallot S. — Inégalités isopérimétriques, courbure de Ricci et invariants géométriques I, C. R. Acad. Sci. Sér. I Math., 296 (1983), 333-335. | Zbl 0535.53034

[GT5] Gallot S. — Inégalités isopérimétriques, courbure de Ricci et invariants géométriques II, C. R. Acad. Sci. Sér. I Math., 296 (1983), 365-368. | Zbl 0535.53035

[GT6] Gallot S. — Isoperimetric inequalities based on integral norms of Ricci curvature, Colloque en l'honneur de Paul Lévy (Ecole Polytechnique, juin 1987), to appear in Astérisque. | Zbl 0665.53041

[GV1] Gromov M. — (rédigé par J. Lafontaine et P. Pansu); Structures métriques pour les variétés riemanniennes, Textes Math. n° 1, 1981. | Zbl 0509.53034

[GV2] Gromov M. — Paul Levy's isoperimetric inequality, Preprint I.H.E.S., 1980.

[GV3] Gromov M. — Curvature, Diameter And Betti Number, Comment. Math. Helv., 56 (1981), 179-197. | Article | Zbl 0467.53021

[H-K] Heintze E., Karcher H. — A general comparison theorem with applications to volume estimates for submanifolds, Ann. Sci. École Norm. Sup., 11 (1978), 451-470. | Article | Zbl 0416.53027

[KN1] Krahn E. — Über Eine Von Rayleigh Formulierte Minimaleigenschaft Des Kreises, Math. Ann., 94 (1924), 97-100. | Article | JFM 51.0356.05

[KN2] Krahn E. — Über Minimaleigenschaften der Kugel in drei und mehr dimensionen, Acta Comm. Univ. Tartu (Dorpat), A9 (1926), 1-44. | JFM 52.0510.03

[LE] Lévy P. — Problèmes concrets d'analyse fonctionnelle, Gauthier-Villars, Paris, 1951. | Zbl 0043.32302

[LI] Li P. — On the Sobolev Constant and the $p$ -spectrum of a compact Riemannian Manifold, Ann. Sci. École Norm. Sup., 13 (1981), 451-457. | Article | Zbl 0466.53023

[L-Y] Li P., Yau S. T.— Estimates of eigenvalues of a compact riemannian manifold, Proc. Sympos. Pure Math., 36 (1980), 205-209. | Article | Zbl 0441.58014

[ME] Meyer D.— Un lemme de géométrie hilbertienne et des applications à la géométrie riemannienne, C. R. Acad. Sci. Sér. I Math., 295 (1982), 467-469. | Zbl 0515.53039

[MI] Massari U. — Esistenza e Regolaritá delle Ipersuperfici di Curvatura Media Assegnata in $𝐑^{n}$ , Arch. Rat. Mech. Anal., 55 (1974), 357-382. | Article | Zbl 0305.49047

[M-F] Morse P., Feshbach. — Methods of theoritical Physics, Mc Graw-Hill, 1953. | Zbl 0051.40603

[MO] Moser J. — On The Volume Element On A Manifold, Trans. Amer. Math. Soc, 120 (1965), 286-294. | Article | Zbl 0141.19407

[M-S] Mckean H. P., Singer I. M. — Curvature and the eigenvalues of the Laplacian, J. Differential Geom., 1 (1967), 43-69. | Article | Zbl 0198.44301

[ON] Osserman R. — The Isoperimetric inequality, Bull. Amer. Math. Soc, 84 (1978), 1183-1238 | Article | Zbl 0411.52006

[PE] Payen L. E. — Isoperimetric inequalities and their applications, SIAM Rev., vol. 9, 3 (1967), 453-488 | Article | Zbl 0154.12602

[P-S] Polya G., Szego G.— Isoperimetric inequalities in Mathematical Physics, Ann. of Math. Stud. 77, 1953. | Zbl 0044.38301

[R-S] Reed M., Simon B.— Methods of Modern Mathematical Physics, vol. I à IV, Acad. Press, 1978. | Zbl 0401.47001

[SP] Spivak M. — A comprehensive introduction to differential geometry, Publish or Perish Inc., (5 volumes). | Zbl 0439.53005

[TA] Talenti G. — Elliptic equations and rearrangements, Ann. Scuola Norm. Sup. Pisa, 3 (1976), 697-718. | Zbl 0341.35031

[WL] Weyl H.— Das Asymptotische Verteilungsgesetz Der Eigenwerte Linearer Partieller Differentialgleichungen, Math. Ann., 71 (1912), 441-469. | Article | JFM 43.0436.01