Minorations sur le λ 1 des variétés riemanniennes

Sylvestre Gallot

Séminaire Bourbaki (1980-1981)

  • Volume: 23, page 132-148
  • ISSN: 0303-1179

How to cite

top

Gallot, Sylvestre. "Minorations sur le $\lambda _1$ des variétés riemanniennes." Séminaire Bourbaki 23 (1980-1981): 132-148. <http://eudml.org/doc/109967>.

@article{Gallot1980-1981,
author = {Gallot, Sylvestre},
journal = {Séminaire Bourbaki},
keywords = {first eigenvalue of the Laplacian; minimum principle; Ricci curvature; isoperimetric inequalities; Dirichlet problem},
language = {fre},
pages = {132-148},
publisher = {Springer-Verlag},
title = {Minorations sur le $\lambda _1$ des variétés riemanniennes},
url = {http://eudml.org/doc/109967},
volume = {23},
year = {1980-1981},
}

TY - JOUR
AU - Gallot, Sylvestre
TI - Minorations sur le $\lambda _1$ des variétés riemanniennes
JO - Séminaire Bourbaki
PY - 1980-1981
PB - Springer-Verlag
VL - 23
SP - 132
EP - 148
LA - fre
KW - first eigenvalue of the Laplacian; minimum principle; Ricci curvature; isoperimetric inequalities; Dirichlet problem
UR - http://eudml.org/doc/109967
ER -

References

top
  1. [AG] S. Agmon, Lectures on Elliptic Boundary value Problems, Van Nostrand, 1965. Zbl0142.37401MR178246
  2. [AU] T. Aubin, Fonction de Green et valeurs propres du laplacien, J. Math. Pures et Appl.1974, 347-371. Zbl0295.35016MR358875
  3. [BE] P. Berard, Spectres et Groupes cristallographiques I : Domaines Euclidiens, Inventiones Math., 58, 1980, 179-199. Zbl0434.35068MR570879
  4. [BB] L. Bérard Bergery, La courbure scalaire des variétés riemanniennes, Séminaire Bourbaki79/80, n° 556. Zbl0461.53023
  5. [B-C] R.L. Bishop et R.J. Crittenden, Geometry of Manifolds, Academic Press (1964). Zbl0132.16003MR169148
  6. [B-G-M] M. Berger, P. Gauduchon et E. Mazet, le spectre d'une variété riemannienne, Lectures Notes in Maths, 194 (1971). Zbl0223.53034
  7. [B-L] H.J. Brascamp et E.H. Lieb, Some Inequalities for Gaussian measures and the long-range order of the one-dimensional plasma, Clarendon Press, Oxford1975. Zbl0348.26011
  8. [BU1] P. Buser, On cheeger's Inequality λ1 ≥ h2/4, Proceedings of A.M.S. Symposia in Pure Maths, 36, 1980. Zbl0432.58024
  9. [C] J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, Problems in Analysis, Princeton University Press, 1970, 195-199. Zbl0212.44903MR402831
  10. [CG] S.Y. Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z.143(1975), 289-297. Zbl0329.53035MR378001
  11. [G1] M. Gromov, Paul Levy's isoperimetric inequality, soumis à Ann. Scient. Ec. Norm. Sup. Paris. 
  12. [G2] M. Gromov, Structures métriques pour les variétés riemanniennes, Cedic-Nathan, textes mathématiques n°1, Paris1981. Zbl0509.53034MR682063
  13. [H-K] 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. Zbl0416.53027MR533065
  14. [M] J. Milnor, Morse theory, Annals of Math. Studies, 53, Princeton University Press, Princeton1963. Zbl0108.10401MR163331
  15. [M-F] P. Morse et Feshbach, Methods of theoritical Physics, Mc-Graw Hill, 1953. Zbl0051.40603
  16. [01] R. Osserman, The Isoperimetric Inequality, Bull. A. M. S., 84, N°6, 1978, 1182-1238. Zbl0411.52006MR500557
  17. [02] R. Osserman, A note on Hayman's theorem on the bass note of a drum, Comment. Math. Helv.52, 1977, 545-555. Zbl0374.52008MR459099
  18. [03] R. Osserman, Bonnesen-style isoperimetric inequalities, American Math. Monthly, 86, 1979, 1-29. Zbl0404.52012MR519520
  19. [P] L.E. Payne, Isoperimetric inequalities and their applications, SIAM Review, Vol 9, N°3, 1967, 453-488. Zbl0154.12602MR218975
  20. [P-W] L.E. Payne et H.F. Weinberger, An optimal Poincaré inequality for convex domains, Arch. Ration. Mech. Anal., 5(1960), 286-292. Zbl0099.08402MR117419
  21. [P-S] G. Polya et G. Szego, Isoperimetric inequalities in mathematical physics, Annals of Math. Studies N°77, Princeton University Press, Princeton1951. Zbl0044.38301MR43486
  22. [W] H.F. Weinberger, An isoperimetric inequality for the N-dimensional free membrane problem, J. Ration. Mech. Anal.5(1956), 533-636. Zbl0071.09902MR79286
  23. [Y] S.T. Yau, Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold, Ann. Sc. Ec. Norm. Sup. Paris8(1975), 487-507. Zbl0325.53039MR397619
  24. [Y-L] 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. Zbl0441.58014MR573435
  25. [BU2] P. Buser, A note on the isoperimetric constant, preprint. MR683635

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.