The first eigenvalue of a closed manifold with positive Ricci curvature

Ling, Jun

doi:10.1090/S0002-9939-06-08332-8

The first eigenvalue of a closed manifold with positive Ricci curvature
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Proc. Amer. Math. Soc. 134 (2006), 3071-3079 Request permission

Abstract:

We give a new estimate on the lower bound for the first positive eigenvalue of the Laplacian on a closed manifold with positive Ricci curvature in terms of the lower bound of the Ricci curvature and the largest interior radius of the nodal domains of eigenfunctions of the eigenvalue.

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