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arXiv:0906.2043 [math.AP]AbstractReferencesReviewsResources

Some inequalities and asymptotic formulas for eigenvalues on Riemannian manifolds

Genqian Liu

Published 2009-06-11Version 1

In this paper, we establish sharp inequalities for four kinds of classical eigenvalues on a bounded domain of a Riemannian manifold. We also establish asymptotic formulas for the eigenvalues of the buckling and clamped plate problems. In addition, we give a negative answer to the Payne conjecture for the one-dimensional case.

Categories: math.AP, math.DG
Subjects: 35P15, 35P20, 58J50
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