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Science in China Series A: Mathematics

, Volume 42, Issue 9, pp 897–904 | Cite as

Eigenvalue estimate on a compact Riemann manifold

  • Zhao Di 
Article

Abstract

LetM be a compact Riemann manifold with the Ricci curvature ≽ - R(R = const. > 0) . Denote by d the diameter ofM. Then the first eigenvalue λ1 ofM satisfies\(\lambda _1 \geqslant \frac{{\pi ^2 }}{{d^2 }} - 0.52R\). Moreover if\(R \leqslant \frac{{5\pi ^2 }}{{3d^2 }}\), then\(\lambda _1 \geqslant \frac{{\pi ^2 }}{{d^2 }} - \frac{R}{2}\)

Keywords

Riemann manifold eigenvalue Ricci curvature 

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References

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Copyright information

© Science in China Press 1999

Authors and Affiliations

  • Zhao Di 
    • 1
  1. 1.Institute of MathematicsChinese Academy of SciencesBeijingChina

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