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Exponential growth and the spectrum of the Laplacian


Author: Robert Brooks
Journal: Proc. Amer. Math. Soc. 82 (1981), 473-477
MSC: Primary 58G25; Secondary 58G11
DOI: https://doi.org/10.1090/S0002-9939-1981-0612743-3
MathSciNet review: 612743
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Abstract: Conditions are given on a noncompact manifold which allow one to conclude that 0 is in the spectrum of the Laplacian on $ M$.


References [Enhancements On Off] (What's this?)

  • [1] R. Brooks, The fundamental group and the spectrum of the Laplacian (to appear). MR 656213 (84j:58131)
  • [2] J. Cheeger and S. T. Yau, A lower bound for the heat kernel (preprint). MR 615626 (82i:58065)
  • [3] S. Y. Cheng and S. T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), 333-354. MR 0385749 (52:6608)
  • [4] H. Donnelly, Asymptotic expansions for the compact quotients of properly discontinuous group actions, Illinois J. Math. 23 (1979), 485-496. MR 537804 (80h:58049)
  • [5] -, Stability theorems for the continuous spectrum of a negatively curved manifold (preprint).
  • [6] F. P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Reinhold, New York, 1969. MR 0251549 (40:4776)
  • [7] H. P. McKean, An upper bound to the spectrum of $ \Delta $ on a manifold of negative curvature, J. Differential Geom. 4 (1970), 359-376. MR 0266100 (42:1009)
  • [8] J. Milnor, A note on curvature and the fundamental group, J. Differential Geom. 2 (1968), 1-7. MR 0232311 (38:636)
  • [9] R. Bishop and R. J. Crittenden, Geometry of manifolds, Academic Press, New York, 1964. MR 0169148 (29:6401)
  • [10] S. T. Yau, Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold, Ann. Sci. Ecole Norm. Sup. 8 (1975), 487-507. MR 0397619 (53:1478)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0612743-3
Article copyright: © Copyright 1981 American Mathematical Society

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