Estimates of eigenvalues of a clamped problem

Tao Zheng

doi:10.2996/kmj/1436403889

Estimates of eigenvalues of a clamped problem

Tao Zheng^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, for the eigenvalue problem of a clamped plate problem on complex projective space with holomorphic sectional curvature c(> 0) and n(≥3)-dimensional noncompact simply connected complete Riemannian manifold with sectional curvature Sec satisfying -a²≤ Sec ≤ -b², where a ≥ b ≥ 0 are constants, we obtain universal eigenvalue inequalities. Moreover, we deduce the estimates of the upper bounds of eigenvalues.

Original language	English
Pages (from-to)	249-269
Number of pages	21
Journal	Kodai Mathematical Journal
Volume	38
Issue number	2
DOIs	https://doi.org/10.2996/kmj/1436403889
Publication status	Published - 11 Jul 2015

Keywords

Biharmonic operator
Complex projective space
Eigenvalue
Hermitian metric
Hyperbolic space

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keywords = "Biharmonic operator, Complex projective space, Eigenvalue, Hermitian metric, Hyperbolic space",

author = "Tao Zheng",

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AB - In this paper, for the eigenvalue problem of a clamped plate problem on complex projective space with holomorphic sectional curvature c(> 0) and n(≥3)-dimensional noncompact simply connected complete Riemannian manifold with sectional curvature Sec satisfying -a2≤ Sec ≤ -b2, where a ≥ b ≥ 0 are constants, we obtain universal eigenvalue inequalities. Moreover, we deduce the estimates of the upper bounds of eigenvalues.

KW - Biharmonic operator

KW - Complex projective space

KW - Eigenvalue

KW - Hermitian metric

KW - Hyperbolic space

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JO - Kodai Mathematical Journal

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Estimates of eigenvalues of a clamped problem

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