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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The first eigenvalue of a closed manifold with positive Ricci curvature


Author: Jun Ling
Journal: Proc. Amer. Math. Soc. 134 (2006), 3071-3079
MSC (2000): Primary 58J50, 35P15; Secondary 53C21
Published electronically: May 1, 2006
MathSciNet review: 2231634
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Jun Ling
Affiliation: Department of Mathematics, Utah Valley State College, Orem, Utah 84058
Email: lingju@uvsc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08332-8
PII: S 0002-9939(06)08332-8
Keywords: Eigenvalue, lower bound, closed Riemannian manifold
Received by editor(s): October 15, 2004
Received by editor(s) in revised form: April 28, 2005
Published electronically: May 1, 2006
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2006 American Mathematical Society