The Estimate of the First Eigenvalue of a Compact Riemannian Manifold
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.
KeywordsRiemannian Manifold Laplace Operator Ricci Curvature Compact Riemannian Manifold Riemann Curvature Tensor
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