Skip to main content
SpringerLink
Log in

The differential form spectrum of hyperbolic space

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

Let Hn+1 denote the simply connected complete space of constant curvature −1. The Laplacian Δ, acting on square integrable p-forms of H, is identified up to unitary equivalence.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bishop, R., Crittenden, R.: Geometry of Manifolds. Academic Press, New York, London, 1964

    Google Scholar 

  2. Cheeger, J.: Spectral Geometry of Spaces with Cone-Like Singularities. Preprint

  3. Chernoff, P.: Essential Self Adjointness of Powers of Generators of Hyperbolic Equations. J. Functional Analysis. 12, 401–414 (1973)

    Google Scholar 

  4. Coddington, E., Levinson, N.: Theory of Ordinary Differential Equations. Mc-Graw Hill, New York, Toronto, London, 1955

    Google Scholar 

  5. Dodziuk, J.: L2 Harmonic Forms on Rotationally Symmetric Riemannian Manifolds. Proc. Amer. Math. Soc.77, 395–400 (1979)

    Google Scholar 

  6. Hartman, P.: Ordinary Differential Equations. J. Wiley and Sons, New York, London, Sydney, 1964

    Google Scholar 

  7. Helgason, S.: Functions on Symmetric Spaces, Harmonic Analysis on Homogeneous Spaces, Proceedings of Symposia in Pure Math., Vol. XXVI. Amer. Math. Soc., Providence, 101–146 (1973)

    Google Scholar 

  8. Kuroda, S. T.: Scattering Theory for Differential Operators I. J. Math. Soc. Japan.25, 75–104 (1973)

    Google Scholar 

  9. McKean, H. P.: An Upper Bound for the Spectrum of Δ on a Manifold of Negative Curvature. J. Diff. Geometry. 4, 359–366 (1970)

    Google Scholar 

  10. Pinsky, M.: The Spectrum of the Laplacian on a Manifold of Negative Curvature. J. Diff. Geometry. 13, 87–91 (1978)

    Google Scholar 

  11. Reed, M., Simon, B.: Methods of Modern Mathematical Physics IV, Analysis of Operators. Academic Press, New York, San Francisco, London, 1978

    Google Scholar 

  12. Rham, Georges de: Varietés Differentiables. Hermann, Paris, 1960

    Google Scholar 

  13. Rudin, W.: Functional Analysis. Mc-Graw Hill, New York, 1973

    Google Scholar 

  14. Yau, S. T.: Isoperimetric Constants and the First Eigenvalue of a Compact Riemannian Manifold. Ann. Sci. Ecole Norm. Sup., IV. Sér.8, 487–507 (1975)

    Google Scholar 

  15. Zucker, S.: Hodge Theory with Degenerating Coefficients: L2 Cohomology in the Poincaré Metric. Ann. of Math., II. Sér.109, 415–476 (1979)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Purdue University, 47907, West Lafayette, Indiana

    Harold Donnelly

Authors
  1. Harold Donnelly
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Donnelly, H. The differential form spectrum of hyperbolic space. Manuscripta Math 33, 365–385 (1981). https://doi.org/10.1007/BF01798234

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01798234

Keywords

Search

Navigation