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.
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References
P. Li, Ann. of Math. Stud., Vol. 102, pp. 73–85. Princeton University Press (1982).
P. Li and S. T. Yau, Proc. Symp. Pure Math., Vol. 36, 1980.
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© 1991 Plenum Press, New York
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Wu, HH. (1991). The Estimate of the First Eigenvalue of a Compact Riemannian Manifold. In: Wu, HH. (eds) Contemporary Geometry. The University Series in Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-7950-8_16
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DOI: https://doi.org/10.1007/978-1-4684-7950-8_16
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