Commentarii Mathematici Helvetici

, Volume 55, Issue 1, pp 347–363 | Cite as

Eigenvalue estimates on homogeneous manifolds

  • Peter Li


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Cheeger,A lower bound for the smallest eigenvalue of the Laplacian, in “Problems in Analysis, A Symposium in Honor of S. Bochner,” Princeton University Press (1970).Google Scholar
  2. [2]
    S. Y. Cheng,Eigenfunctions and eigenvalues of Laplacian, Proc. of Sym. Pure Math.,27 (1975), 185–193.Google Scholar
  3. [3]
    —,Eigenvalue comparison theorems and its geometric applications, Math. Z.,143 (1975), 289–297.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    S. Gallot etD. Meyer,Opérateur de Courbure et Laplacien des formes différentielles d'une variété Riemannienne, J. Math. pures et appl.,54 (1975), 259–284.MathSciNetGoogle Scholar
  5. [5]
    B. Lawson,Lectures on Minimal Submanifolds, I.M.P.A. Rio de Janeiro (1973).Google Scholar
  6. [6]
    P. Li,On the First Eigenvalue and Eigenfunctions of the Laplace Operator on a Compact Riemannian Manifold and their Geometric Applications, Ph.D. Thesis, Berkeley (1979).Google Scholar
  7. [7]
    P. Li,A lower bound for the first eigenvalue of the Laplacian on a compact manifold, Indiana J. Math., to appear.Google Scholar
  8. [8]
    P. Li,On the Sobolev constant and the p-spectrum of a compact Riemannian manifold, to appear.Google Scholar
  9. [9]
    P. Li, andS. T. Yau,Estimates of eigenvalues of a compact Riemannian manifold, to appear.Google Scholar
  10. [10]
    L. E. Payne, G. Pólya andH. F. Weinberger,On the ratio of consecutive eigenvalues, J. Math. Phys.,35 (1956), 289–298.MathSciNetGoogle Scholar
  11. [11]
    P. Yang andS. T. Yau,Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds, preprint.Google Scholar
  12. [12]
    S. T. Yau Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold, Ann. Scient. Ec. Norm. Sup. 4 series, t.8 (1975), 487–507.MATHGoogle Scholar

Copyright information

© Birkhäuser Verlag 1980

Authors and Affiliations

  • Peter Li
    • 1
  1. 1.The Institute for Advanced StudyPrinceton

Personalised recommendations