Skip to main content

Minorations sur le λ1 des variétés riemanniennes

  • Conference paper
  • First Online:
Séminaire Bourbaki vol. 1980/81 Exposés 561–578

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 901))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Références

  1. S. AGMON, Lectures on Elliptic Boundary value Problems, Van Nostrand, 1965.

    Google Scholar 

  2. T. AUBIN, Fonction de Green et valeurs propres du laplacien, J. Math. Pures et Appl. 1974, 347–371.

    Google Scholar 

  3. P. BERARD, Spectres et Groupes cristallographiques I: Domaines Euclidiens, Inventiones Math., 58, 1980, 179–199.

    Article  MathSciNet  MATH  Google Scholar 

  4. L. BÉRARD BERGERY, La courbure scalaire des variétés riemanniennes, Séminaire Bourbaki 79/80, no 556.

    Google Scholar 

  5. R.L. BISHOP et R.J. CRITTENDEN, Geometry of Manifolds, Academic Press (1964).

    Google Scholar 

  6. M. BERGER, P. GAUDUCHON et E. MAZET, le spectre d'une variété riemannienne, Lectures Notes in Maths, 194 (1971).

    Google Scholar 

  7. H.J. BRASCAMP et E.H. LIEB, Some Inequalities for Gaussian measures and the long-range order of the one-dimensional plasma, Clarendon Press, Oxford 1975.

    Google Scholar 

  8. P. BUSER, On cheeger's Inequality λ12/4, Proceedings of A.M.S. Symposia in Pure Maths, 36, 1980.

    Google Scholar 

  9. J. CHEEGER, A lower bound for the smallest eigenvalue of the Laplacian, Problems in Analysis, Princeton University Press, 1970, 195–199.

    Google Scholar 

  10. S.Y. CHENG Eigenvalue comparison theorems and its geometric applications, Math. Z. 143(1975), 289–297.

    Article  MathSciNet  MATH  Google Scholar 

  11. M. GROMOV, Paul Levy's isoperimetric inequality, soumis à Ann. Scient. Ec. Norm. Sup. Paris.

    Google Scholar 

  12. M. GROMOV, Structures métriques pour les variétés riemanniennes, Cedic-Nathan, textes mathématiques no1, Paris 1981.

    Google Scholar 

  13. E. HEINTZE et H. KARCHER, A general comparison theorem with applications to volume estimates for submanifolds, Ann. Scient. Ec. Norm. Sup. Paris, 11, 1978, 451–470.

    MathSciNet  MATH  Google Scholar 

  14. J. MILNOR, Morse theory, Annals of Math. Studies, 53, Princeton University Press, Princeton 1963.

    MATH  Google Scholar 

  15. P. MORSE et FESHBACH, Methods of theoritical Physics, Mc-Graw Hill, 1953.

    Google Scholar 

  16. R. OSSERMAN, The Isoperimetric Inequality, Bull. A. M. S., 84, No6, 1978, 1182–1238.

    Article  MathSciNet  MATH  Google Scholar 

  17. R. OSSERMAN, A note on Hayman's theorem on the bass note of a drum, Comment. Math. Helv. 52, 1977, 545–555.

    MathSciNet  MATH  Google Scholar 

  18. R. OSSERMAN, Bonnesen-style isoperimetric inequalities, American Math. Monthly, 86, 1979, 1–29.

    Article  MathSciNet  MATH  Google Scholar 

  19. L.E. PAYNE, Isoperimetric inequalities and their applications, SIAM Review, Vol 9, No3, 1967, 453–488.

    Article  MathSciNet  MATH  Google Scholar 

  20. L.E. PAYNE et H.F. WEINBERGER, An optimal Poincaré inequality for convex domains, Arch. Ration. Mech. Anal., 5 (1960), 286–292.

    Article  MathSciNet  MATH  Google Scholar 

  21. G. POLYA et G. SZEGO Isoperimetric inequalities in mathematical physics, Annals of Math. Studies No77, Princeton University Press, Princeton 1951.

    MATH  Google Scholar 

  22. H.F. WEINBERGER, An isoperimetric inequality for the N-dimensional free membrane problem, J. Ration. Mech. Anal. 5 (1956), 533–636.

    MathSciNet  Google Scholar 

  23. S. T. YAU, Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold, Ann. Sc. Ec. Norm. Sup. Paris 8 (1975), 487–507.

    MATH  Google Scholar 

  24. S.T. YAU et P. LI, Estimates of eigenvalues of a compact Riemannian manifold, Proc. Symp. Pure Math. A. M. S., 36 (1980), 205–239.

    MathSciNet  Google Scholar 

  25. P. BUSER, A note on the isoperimetric constant, preprint.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1981 N. Bourbaki

About this paper

Cite this paper

Gallot, S. (1981). Minorations sur le λ1 des variétés riemanniennes. In: Séminaire Bourbaki vol. 1980/81 Exposés 561–578. Lecture Notes in Mathematics, vol 901. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0097194

Download citation

  • DOI: https://doi.org/10.1007/BFb0097194

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11176-4

  • Online ISBN: 978-3-540-38956-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics