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A note on the first nonzero eigenvalue of the laplacian acting on P-forms

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Bibliography

  • [BR] E. Brieskorn, Beispiele zur Differentialtopologie von Singularitäten, Invent Math 2 (1966) p. 1–14

    Article  MATH  MathSciNet  Google Scholar 

  • [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

    Article  MATH  MathSciNet  Google Scholar 

  • [BD] P.Bérard: Spectral geometry: Direct and inverse problems; Lect.notes in Math. 1207; Springer 1986

  • [B-G] P.Bérard—S.Gallot, Inégalités isopérimétriques pour l'équation de la chaleur et application a l'estimation de quelques invariants, Séminaire Goulaouic-Meyer-Schwartz 1983–1984

  • [B-G-M] M. Berger—P. Gauduchon—E. Mazet, Le spectre d'une variété riemannienne, Lect. Notes in Math. 194, (1971)

  • [BU1] P. Buser, On Cheeger Inequality λ1 ≥ h 2/4, Proc. of Symp. in Pure Math. 36 p. 29–77 (1980)

    MathSciNet  Google Scholar 

  • [BU2] P. Buser, A note on the isoperimetric constant, Ann. Scient. Ec. Norm. Sup. Série4, t. 15, (1982) P.213–230

    MATH  MathSciNet  Google Scholar 

  • [C-G1] J. Cheeger—Gromov, M., Collapsing Riemanniann manifolds while keeping their curvature bounded I, J. diff. Geom. 23 (1986) 309–346

    MATH  MathSciNet  Google Scholar 

  • [C-G2] J. Cheeger, M. Gromov: Collapsing Riemanniann manifold while keeping their curvature bounded II, Preprint

  • [CR] J. Cheeger. A lower bound for the smallest eigenvalue of the Laplacian, problems in Analysis, A symposium in honour of Bochner, Princeton University Press, N.J. p. 195–199 (1970)

    Google Scholar 

  • [CS] G.Courtois, Thesis, Université de Grenoble, 1987

  • [GA1] S. Gallot: Inégalités isopérimétriques courbure de Ricci et invariants géométriques I, C.A. Acad. Sci. Paris 296, série I, 1983, p. 333–336

    MATH  MathSciNet  Google Scholar 

  • [GA2] S. Gallot: Inégalités isopérimétriques, courbure de Ricci et invariants géométriques II, C.R. Acad. Sci. Paris 296, série I, 1983, p. 365–368

    MATH  MathSciNet  Google Scholar 

  • [GA3] S. Gallot, A Sobolev inequality and some geometric applications, Spectra of Riemannian manifolds (actes du colloque de Kyoto 1981), Kayai Publ. 1983, p. 45–55

  • [GH] P. Ghanaat, Almost Lie groups of type ℝn, to appear at Journal für die reine und angewandte Mathematik

  • [G-M] S. Gallot,—D. Meyer, Opérateur de courbure et Laplacien des formes différentielles d'une variété riemannienne, J. Math., pures et appl. 54 (1975) 259–284

    MathSciNet  Google Scholar 

  • [GR1] M. Gromov, Hyperbolic manifolds according to Thurston and Jorgensen, Séminaire Bourbaki no 546 (1979–80)

  • [GR2] M. Gromov, Volume and bounded cohomology, I.H.E.S. 1982, P.5–100

  • [GR3] M. Gromov, Structures métriques pour les variétés riemanniennes, Réd. par J. Lafontaine et P. Pansu, Paris 1981

    MATH  Google Scholar 

  • [K] A. Katsuda, Gromov's convergence theorem and its application, Nagoya, Math. J. 100 (1985) p. 11–48

    MATH  MathSciNet  Google Scholar 

  • [Li] P. Li, On the Sobolev constant and the p-spectrum of a compact Riemannian manifold. Ann. scient. Ec. Norm. Sup. Série 4, t. 13, (1980) 451–469

    MATH  Google Scholar 

  • [MI] J.Milnor, On the 3-dimensional Brieskorn manifolds M(p,q,r). In knots, groups and 3-manifolds, Ann. Math., Studies, Princeton University Press 84, (1975)

  • [PA] P. Pansu, Dégénérescence des variétés riemanniennes d'après J. Cheeger et M. Gromov, Astérisque 121 (1985)

  • [PE] S. Peters, Convergence of Riemanniann manifolds compositio, Math. 62 (1987) p. 1–16

    Google Scholar 

  • [SN] R. Schoen, A lower bound for the first eigenvalue of a negatively curved manifold, J. Differential Geometry 17 (1982) P.233–238

    MATH  MathSciNet  Google Scholar 

  • [ST] P. Scott, The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983) 401–487

    Article  MATH  MathSciNet  Google Scholar 

  • [T] N. Teleman, The index of signature operators on Lipschitz manifolds, Pub. Math IHES 58 (1983) p: 39–78

    MathSciNet  Google Scholar 

  • [TH] W. Thurston, The geometry and topology of 3-manifolds, Lecture notes from Princeton University, (1977–78)

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The first author was supported by the Swiss National Sciences Foundation and the second author was partially supported by contrat CEE GADGET.SC1-0105-C.

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Colbois, B., Courtois, G. A note on the first nonzero eigenvalue of the laplacian acting on P-forms. Manuscripta Math 68, 143–160 (1990). https://doi.org/10.1007/BF02568757

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  • DOI: https://doi.org/10.1007/BF02568757

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