Some inequalities and asymptotic formulas for eigenvalues on Riemannian manifolds

Genqian Liu

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arXiv · 0906.2043

Some inequalities and asymptotic formulas for eigenvalues on Riemannian manifolds

Genqian Liu

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Abstract

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.

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Genqian Liu. 2009-06-11. Some inequalities and asymptotic formulas for eigenvalues on Riemannian manifolds. https://arxiv.org/abs/0906.2043

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