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The Estimate of the First Eigenvalue of a Compact Riemannian Manifold

  • Hung-Hsi Wu
Part of the The University Series in Mathematics book series (USMA)

Abstract

The main theorem proved in this chapter is: Let M be a compact Riemannian manifold with nonnegative Ricci curvature. Then the first eigenvalue −λ1 of the Laplace operator of M satisfies λ1≥π2/ d2 , where d denotes the diameter of M. This estimate improves the recent results due to S. T. Yau and P. Li [1, 2] and gives the best estimate for this kind of manifold.

Keywords

Riemannian Manifold Laplace Operator Ricci Curvature Compact Riemannian Manifold Riemann Curvature Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P. Li, Ann. of Math. Stud., Vol. 102, pp. 73–85. Princeton University Press (1982).Google Scholar
  2. 2.
    P. Li and S. T. Yau, Proc. Symp. Pure Math., Vol. 36, 1980.Google Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Hung-Hsi Wu
    • 1
  1. 1.University of CaliforniaBerkeleyUSA

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