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Annals of Global Analysis and Geometry

, Volume 15, Issue 1, pp 27–44 | Cite as

Small Eigenvalues of the Laplacians on Vector Bundles over Towers of Covers

  • Wing-Keung To
Article
  • 55 Downloads

Abstract

Under the conditions that a compact Riemannian manifold is of sufficiently pinched negative sectional curvature and that a smooth Hermitian vector bundle over the manifold is also of sufficiently small curvature, we prove some pinching results on the asymptotic behavior of the numbers of small eigenvalues of the Laplacians on the induced Hermitian vector bundles over a tower of covers of the manifold. In the process we also obtain interesting results on the non-existence of square integrable 'almost harmonic' vector bundle-valued forms omitting the middle degree(s) on the universal cover.

asymptotic formulas eigenvalues harmonic forms towers of covers 

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Wing-Keung To
    • 1
  1. 1.Department of MathematicsNational University of SingaporeSingapore

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