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The first eigenvalue in a tower of coverings
Author(s):
Robert
Brooks
Journal:
Bull. Amer. Math. Soc.
13
(1985),
137-140.
MSC (1980):
Primary 58F19
MathSciNet review:
799796
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Additional information
References:
- 1.
- R. Brooks, Amenability and the spectrum of the Laplacian, Bull. Amer. Math. Soc. (N. S.) 6 (1982), 87-89. MR 634438
- 2.
- R. Brooks, The bottom of the spectrum of a Riemannian covering, J. Reine Angew. Math. 357 (1985), 101-114. MR 783536
- 3.
- R. Brooks, The fundamental group and the spectrum of the Laplacian, Comment. Math. Helv. 56 (1981), 581-596. MR 656213
- 4.
- R. Brooks, The spectral geometry of the Appollonian packing, Comm. Pure Appl. Math. (to appear). MR 792395
- 5.
- P. Buser, A note on the isoperimetric constant, Ann. Sci. École Norm. Sup. 15 (1982), 213-230. MR 683635
- 6.
- P. Buser, On Cheeger's inequality λ, Proc. Sympos. Pure Math., vol. 36, Amer. Math. Soc., Providence, R.I., 1980, pp. 29-77. MR 573428
- 7.
- B. Randol, Small eigenvalues of the Laplace operator on compact Riemann surfaces, Bull. Amer. Math. Soc. 80 (1974), 996-1000. MR 400316
- 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. MR 750670
- 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. MR 182610
- 10.
- T. Sunada, Riemannian coverings and isospectral manifolds, Ann. of Math. (2) 121 (1985), 169-186. MR 782558
- 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. MR 402831
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Additional Information:
DOI:
10.1090/S0273-0979-1985-15397-2
PII:
S 0273-0979(1985)15397-2
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