Skip to main content
Log in

Collapsing of Riemannian manifolds and eigenvalues of Laplace operator

  • Published:
Inventiones mathematicae Aims and scope

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Anné, C.: Lecture at Marseille Luminy (1984)

  2. Beale, J.T.: Scattering Frequency of Resonators. Comm. Pure Appl. Math.26, 549–565 (1973)

    Google Scholar 

  3. Bemelmans, J., Min-Oo, Ruh, E.: Smoothing Riemannian metrics. Math. Z.188, 69–74 (1984)

    Google Scholar 

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

    Google Scholar 

  5. Fukaya, K.: Collapsing Riemannian manifolds to lower dimensional one (to appear in J. Differ. Geom.)

  6. Fukaya, K.: A boundary of the set of Riemannian manifolds with bounded curvatures and diameters (Preprint)

  7. Gallot, S.: Inéqualité isopérimétrique, courbure de Ricci et invariants géometriques II. C.R. Acad. Sc. Paris296, 365–368 (1982)

    Google Scholar 

  8. Gromov, M., Lafontaine, J., Pansu, P.: Structures métriques pour les variétés riemanniennes, Paris: Cedic Fernand/Nathan, 1981

    Google Scholar 

  9. Li, P.: On the Sovolev constant and thep-spectrum of a compact Riemannian manifold. Ann. Sci. Ec. Norm. Super.13, 451–469 (1980)

    Google Scholar 

  10. Mitchel, J.: On Carnot-Carathéodory metrics. J. Differ. Geom.21, 25–45 (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fukaya, K. Collapsing of Riemannian manifolds and eigenvalues of Laplace operator. Invent Math 87, 517–547 (1987). https://doi.org/10.1007/BF01389241

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01389241

Keywords

Navigation