Eigenvalue estimates on domains in complete noncompact riemannian manifolds

Daguang Chen; Tao Zheng; Min Lu

doi:10.2140/pjm.2012.255.41

Eigenvalue estimates on domains in complete noncompact riemannian manifolds

Daguang Chen^*, Tao Zheng, Min Lu

^*Corresponding author for this work

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

10 Citations (Scopus)

Abstract

In this paper, we obtain universal inequalities for eigenvalues of the Dirichlet eigenvalue problem of the Laplacian and the clamped plate problem on a bounded domain in an n-dimensional (n ≥ 3) noncompact simply connected complete Riemannian manifold with sectional curvature Sec satisfying -K ² ≥ Sec ≥ -k ² , where K ≥ k ≥ 0 are constants. When M is ℍ ⁿ(-1) (n≥3), these inequalities become ones previously found by Cheng and Yang.

Original language	English
Pages (from-to)	41-54
Number of pages	14
Journal	Pacific Journal of Mathematics
Volume	255
Issue number	1
DOIs	https://doi.org/10.2140/pjm.2012.255.41
Publication status	Published - 2012
Externally published	Yes

Keywords

Eigenvalues
Laplacian
The clamped plate problem
The dirichlet problem
The universal inequality

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10.2140/pjm.2012.255.41

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abstract = "In this paper, we obtain universal inequalities for eigenvalues of the Dirichlet eigenvalue problem of the Laplacian and the clamped plate problem on a bounded domain in an n-dimensional (n ≥ 3) noncompact simply connected complete Riemannian manifold with sectional curvature Sec satisfying -K 2 ≥ Sec ≥ -k 2 , where K ≥ k ≥ 0 are constants. When M is ℍ n(-1) (n≥3), these inequalities become ones previously found by Cheng and Yang.",

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AU - Chen, Daguang

AU - Zheng, Tao

AU - Lu, Min

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AB - In this paper, we obtain universal inequalities for eigenvalues of the Dirichlet eigenvalue problem of the Laplacian and the clamped plate problem on a bounded domain in an n-dimensional (n ≥ 3) noncompact simply connected complete Riemannian manifold with sectional curvature Sec satisfying -K 2 ≥ Sec ≥ -k 2 , where K ≥ k ≥ 0 are constants. When M is ℍ n(-1) (n≥3), these inequalities become ones previously found by Cheng and Yang.

KW - Eigenvalues

KW - Laplacian

KW - The clamped plate problem

KW - The dirichlet problem

KW - The universal inequality

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DO - 10.2140/pjm.2012.255.41

M3 - Article

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SN - 0030-8730

VL - 255

SP - 41

EP - 54

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 1

ER -

Eigenvalue estimates on domains in complete noncompact riemannian manifolds

Abstract

Keywords

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