Quelques théorèmes d'annulation et de majoration d'invariants géométriques

Pierre Bérard

Mémoires de la Société Mathématique de France (1991)

  • Volume: 46, page 19-26
  • ISSN: 0249-633X

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Bérard, Pierre. "Quelques théorèmes d'annulation et de majoration d'invariants géométriques." Mémoires de la Société Mathématique de France 46 (1991): 19-26. <http://eudml.org/doc/94893>.

@article{Bérard1991,
author = {Bérard, Pierre},
journal = {Mémoires de la Société Mathématique de France},
keywords = {Ricci curvature; Betti numbers; Bochner theorem; Laplacian},
language = {fre},
pages = {19-26},
publisher = {Société mathématique de France},
title = {Quelques théorèmes d'annulation et de majoration d'invariants géométriques},
url = {http://eudml.org/doc/94893},
volume = {46},
year = {1991},
}

TY - JOUR
AU - Bérard, Pierre
TI - Quelques théorèmes d'annulation et de majoration d'invariants géométriques
JO - Mémoires de la Société Mathématique de France
PY - 1991
PB - Société mathématique de France
VL - 46
SP - 19
EP - 26
LA - fre
KW - Ricci curvature; Betti numbers; Bochner theorem; Laplacian
UR - http://eudml.org/doc/94893
ER -

References

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  2. [B-B-G] BÉRARD P., BESSON G., GALLOT S. — Sur une inégalité isopérimétrique qui généralise celle de Paul Lévy-Gromov, Invent. Math., 80 (1985), 25-308. Zbl0571.53027MR86j:58017
  3. [BD] BÉRARD P. — From vanishing theorems to estimating theorems : the Bochner technique revisited, Bull. Amer. Math. Soc., 19 (1988), 371-406. Zbl0662.53037MR89i:58152
  4. [BE] BESSON G. — On symmetrization, Appendix A in Spectral Geometry : direct and inverse problems, P. Bérard, Lecture Notes 1207, Springer, 1986. Zbl0608.58001MR88f:58146
  5. [B-G] BÉRARD P., GALLOT S. — Inégalités isopérimétriques pour l'équation de la chaleur et applications à l'estimation de quelques invariants, Exp. XV, Séminaire Goulaouic-Meyer-Schwartz, 83-84, Ecole Polytechnique, Palaiseau, 1984. Zbl0542.53025MR87d:58142
  6. [BO] BOCHNER S. — Vector fields and Ricci curvature, Bull. Amer. Math. Soc., 52 (1946), 776-797. Zbl0060.38301MR8,230a
  7. [DK] DODZIUK J. — Vanishing theorems for square-integrable harmonic forms, Proc. Indian Acad. Sci. (Math. Sci.), 90 (1981), 21-27. Zbl0479.53035MR83h:58006
  8. [E-L] EELIS J., LEMAIRE L. — Selected topics in harmonic maps, CBMS n° 50, Amer. Math. Soc., 1980. 
  9. [E-R] ELWORTHY K.D., ROSENBERG S. — Compact manifolds with a little negative curvature, Bull. Amer. Math. Soc., 20 (1989), 41-44. Zbl0677.53050MR89g:53062
  10. [GA] GALLOT S. — Isoperimetric inequalities based on integral norms of Ricci curvature, Astérisque Soc. Math. France, 157-158 (1989), 191-216. Zbl0665.53041
  11. [GY] GILKEY P. — The spectral geometry of a Riemannian manifold, J. Differential Geom., 10 (1975), 601-618. Zbl0316.53035MR53 #4150
  12. [LB] LIEB E. — The number of bound states of one-body Schrödinger operators and the Weyl problem, Amer. Math. Soc. Proc. Symp. Pure Math., 36 (1980), 241-252. Zbl0445.58029MR82i:35134
  13. [RO] ROSENBERG S. — Semigroup domination and vanishing theorems, (Proceedings 1987 Cornel Conf. on Geometry of Random Motion) Contemp. Math., 73, Amer. Math. Soc. (1988), 287-302. Zbl0657.53022MR90k:58243
  14. [SI] SIMONS J. — Minimal varieties in Riemannian manifolds, Ann. of Math., 88 (1968), 62-105. Zbl0181.49702MR38 #1617
  15. [SN] SULLIVAN D. — Related aspects of positivity in Riemannian geometry, J. Differential Geom., 25 (1987), 327-351. Zbl0615.53029MR88d:58132
  16. [WU] WU H. — The Bochner technique in differential geometry, Math. Report Series, Harwood Academic Publishers, 1987. 
  17. [YA] YAU S.T. — Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana U. Math. J., 25 (1976), 659-670. Zbl0335.53041MR54 #5502

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