Article PDF
Avoid common mistakes on your manuscript.
References
Berenstein, C., Zalcman, L.: Pompeiu's Problem in Symmetric Spaces. Comment. Math. Helv.55, 593–621 (1980)
Bishop, R., Crittenden, R.: Geometry of Manifolds. New York-London: Academic Press 1964
Brooks, R.: Exponential Growth and the Spectrum of the Laplacian. Proc. Amer. Math. Soc.82, 473–477 (1981)
Brooks, R.: The Fundamental Group and the Spectrum of the Laplacian. Preprint
Cheeger, J.: A Lower Bound for the Smallest Eigenvalue of the Laplacian. In: Problems in analysis (Ed. R.C. Gunning). A Symposium in Honor of Salomon Bochner (Princeton 1969), pp. 195–199. Princeton: Princeton University Press 1970
Cheng, S. Y.: Eigenvalue Comparison Theorems and its Geometric Applications. Math. Z.143, 289–297 (1975)
Donnelly, H.: On the Essential Spectrum of a Complete Riemannian Manifold. Topology20, 1–14 (1981)
Donnelly, H., Li, P.: Pure Point Spectrum and Negative Curvature for Non-Compact Manifolds. Duke Math. J.46, 497–503 (1979)
McKean, H. P. An Upper Bound to the Spectrum of Δ on a Manifold of Negative Curvature. J. Differential Geometry4, 359–366 (1970)
Milnor, J.: A Note on Curvature and Fundamental Group. J. Differential Geometry2, 1–7 (1968)
Pinsky, M.: The Spectrum of the Laplacian on a Manifold of Negative Curvature I. J. Differential Geometry13, 87–91 (1978)
Pinsky, M.: An Improved Bound for the Spectrum of the Laplacian. Preprint
Yau, S. T.: Isoperimetric Constants and the First Eigenvalue of a Complete Riemannian Manifold. Ann. Sci. Ecole Norm. Sup. (4)8, 487–507 (1975)
Baider, A.: Noncompact Manifolds with Discrete Spectra. J. Differential Geometry14, 41–57 (1979)
Author information
Authors and Affiliations
Additional information
Partially supported by National Science Foundation grant MCS7802679
Rights and permissions
About this article
Cite this article
Brooks, R. A relation between growth and the spectrum of the Laplacian. Math Z 178, 501–508 (1981). https://doi.org/10.1007/BF01174771
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01174771