Bulletin (New Series) of the American Mathematical Society

The first eigenvalue in a tower of coverings

Robert Brooks

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc. (N.S.), Volume 13, Number 2 (1985), 137-140.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183552694

Mathematical Reviews number (MathSciNet)
MR799796

Zentralblatt MATH identifier
0579.58031

Subjects
Primary: 58F19

Citation

Brooks, Robert. The first eigenvalue in a tower of coverings. Bull. Amer. Math. Soc. (N.S.) 13 (1985), no. 2, 137--140. https://projecteuclid.org/euclid.bams/1183552694


Export citation

References

  • 1. R. Brooks, Amenability and the spectrum of the Laplacian, Bull. Amer. Math. Soc. (N. S.) 6 (1982), 87-89.
  • 2. R. Brooks, The bottom of the spectrum of a Riemannian covering, J. Reine Angew. Math. 357 (1985), 101-114.
  • 3. R. Brooks, The fundamental group and the spectrum of the Laplacian, Comment. Math. Helv. 56 (1981), 581-596.
  • 4. R. Brooks, The spectral geometry of the Appollonian packing, Comm. Pure Appl. Math. (to appear).
  • 5. P. Buser, A note on the isoperimetric constant, Ann. Sci. École Norm. Sup. 15 (1982), 213-230.
  • 6. P. Buser, On Cheeger's inequality λ1 ≥ h2/4, Proc. Sympos. Pure Math., vol. 36, Amer. Math. Soc., Providence, R.I., 1980, pp. 29-77.
  • 7. B. Randol, Small eigenvalues of the Laplace operator on compact Riemann surfaces, Bull. Amer. Math. Soc. 80 (1974), 996-1000.
  • 8. P. Sarnak, Additive number theory and Maass forms, Lecture Notes in Math., vol. 1052, Springer-Verlag, Berlin and New York, 1984, pp. 286-309.
  • 9. A. Selberg, On the estimation of Fourier coefficients off modular forms, Proc. Sympos. Pure Math., vol. 8, Amer. Math. Soc., Providence, R.I., 1965, pp. 1-15.
  • 10. T. Sunada, Riemannian coverings and isospectral manifolds, Ann. of Math. (2) 121 (1985), 169-186.
  • 11. J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, Problems in Analysis, Princeton Univ. Press, Princeton, N. J., 1970, pp. 195-199.