Le spectre du laplacien agissant sur les p-formes différentielles
Séminaire de théorie spectrale et géométrie, Volume 14 (1995-1996), pp. 25-37. 
@article{TSG_1995-1996__14__25_0,
     author = {Bruno Colbois},
     title = {Le spectre du laplacien agissant sur les $p$-formes diff\'erentielles},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {25--37},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {14},
     year = {1995-1996},
     doi = {10.5802/tsg.164},
     zbl = {0886.58113},
     mrnumber = {1721301},
     language = {fr},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.164/}
}
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Bruno Colbois. Le spectre du laplacien agissant sur les $p$-formes différentielles. Séminaire de théorie spectrale et géométrie, Volume 14 (1995-1996), pp. 25-37. doi : 10.5802/tsg.164. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.164/

[AC95] Anné C., Colbois B. - Spectre du laplacien agissant sur les p-formes différentielles et écrasement d'anses, Math. Ann. 303 ( 1995), 545-573. | MR | Zbl

[BBG85] Bérard P., Besson G., Gallot S. - Sur une inégalité isopérimétrique qui généralise celle de Paul Lévy-Gromov, Invent. Math. 80 ( 1985). 295-308. | MR | Zbl

[BGM71] Berger M., Gauduchon P., Mazet E. - Le spectre d'une variété riemannienne, Springer-Verlag, 1971. | MR | Zbl

[Br86] Brooks R. - The spectral geometry of a tower of covering, J. Differential Geom. 23 ( 1986), 97-107. | MR | Zbl

[BT86] Bott R., Tu L. - Differential forms inalgebraic topology, Springer-Verlag, 1986. | Zbl

[Bu82] Buser P. - A note on the isoperimetric constant, Ann. Sci. École Norm. Sup.Paris 15 ( 1982), 213-230. | Numdam | MR | Zbl

[CC96] Colbois B., Courtois G. - En préparation, 1996.

[CC90] Colbois B., Courtois G. - A note on the first non-zero eigenvalue of the Laplacien acting on p-forms, Manuscripts Math. ( 1990), 143-160. | MR | Zbl

[CD94] Colbois B., Dodziuk J. - Riemannian metrics with large λ1, Proc. Amer. Math. Soc. 122 n° 3 ( 1994), 905-906. | MR | Zbl

[Cg75] Cheng S.Y. - Eigenvalues comparison theorems and its geometric application, Math. Z. 143 ( 1975), 289-297. | MR | Zbl

[Cr68] Cheeger J. - The relation between the Laplacian and the diameter for manifolds of non-negative curvature, Archiv. der Math. XLX ( 1968), 558-560. | MR | Zbl

[Cr70] Cheeger J. - A lower bound for the smallest eigenvalue of the Laplacian, "Problem in AnaJysis" Princeton Univ. Press ( 1970), 195-199. | MR | Zbl

[CE75] Cheeger J., Ebin D. - Comparison theorem in Riemannian geometry, "North-Holland" Publ. Amsterdam, 1975. | MR | Zbl

[CZ95] Cheng X., Zhou D. - First eigenvalue estimate on Riemannian manifolds, Hokkaïdo Mathematical Journal 24 ( 1995), 453-472. | MR | Zbl

[Fo95] Forman R. - Spectral sequences and adiabatic limits, Commun Math. Phys. 168( 1995), 57-116. | MR | Zbl

[Fu90] Fukaya K. - Hausdorff convergence of Riemannian manifolds and its applications, recent topics in differential and analytic geometry, (T.Ochiai ed.) Adv. Stud. Pure Math., Kinohuniya, Tokyo 18 ( 1990),. | MR | Zbl

[Fu87] Fukaya K. - Collapsing Riemannian manifolds to one of lower dimension, J. Differential Geom. 25 ( 1987). 517-547. | MR | Zbl

[Fu89] Fukaya K. - Collapsing Riemannian manifolds to one of lower dimension II, J. Math. Soc. Japan 41 ( 1989), 333-356. | MR | Zbl

[Gr80] Gromov M. - Paul Lévy's isoperimetric inequality, Prépublication IHES, 1980.

[GLP80] Gromov M., Lafontaine J.,Pansu P. - Structure métrique pour les variétés riemanniennes, Cedic-Fernand Nathan, 1980. | Zbl

[GP95] Gentile G., Pagliara V. - Riemannian metrics with large fust eigenvalue on forms of degree p, Proc. Amer. Math. Soc. 123 ( 1995). 3855-3856. | MR | Zbl

[He70] Hersch J. - Quatre propriétés isopérimétriques des membranes sphériques, C. R. Acad. Sci. Paris ( 1970), 1645-1648. | MR | Zbl

[HK78] Heintze E., Karcher H. - A general comparison theorem with applications to volume estimates for submanifolds, Ann. Sci. École Norm. Sup. Paris 11 ( 1978), 451-470. | Numdam | MR | Zbl

[Li58] Lichnerowicz A. - Géométrie des groupes de transformations, Dunod, 1958. | MR | Zbl

[Lo95] Lohkamp I. - Discontinuity of geometric expansions, Preprint, 1995. | Zbl

[Mu80] Muto H. - The first eigenvalue of the Laplacian on even dimensional spheres, Tohoku Math. Journal 32 ( 1980), 427-432. | MR | Zbl

[Pa83] Pansu P. - Effondrement des variétés riemanniennes, Sem. Bourbaki, 618, 1983-84. | Numdam | Zbl

[Ur79] Urakawa H. - On the least eigenvalue of the Laplacian for compact group manifolds, J. Math. Soc. Japan 31 ( 1979). 209-226. | MR | Zbl

[Wa83] Warner F. - Foundation of differentiable manifolds and Lie groups, Springer-Verlag, 1983. | MR | Zbl

[YY80] Yang P., Yau S.T. - Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds, Ann. Scuola Norm. Sup. Pisa 7 ( 1980), 55-63. | Numdam | MR | Zbl

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