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)


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.


Riemannian Manifold Laplace Operator Ricci Curvature Compact Riemannian Manifold Riemann Curvature Tensor 


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  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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