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

^*此作品的通讯作者

Tsinghua University
Chinese Academy of Sciences
Nanjing Audit University

科研成果: 期刊稿件 › 文章 › 同行评审

12 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	41-54
页数	14
期刊	Pacific Journal of Mathematics
卷	255
期	1
DOI	https://doi.org/10.2140/pjm.2012.255.41
出版状态	已出版 - 2012
已对外发布	是

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title = "Eigenvalue estimates on domains in complete noncompact riemannian manifolds",

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.",

keywords = "Eigenvalues, Laplacian, The clamped plate problem, The dirichlet problem, The universal inequality",

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AU - Zheng, Tao

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N2 - 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.

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

UR - https://www.scopus.com/pages/publications/84863002364

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DO - 10.2140/pjm.2012.255.41

M3 - Article

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EP - 54

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 1

ER -

Eigenvalue estimates on domains in complete noncompact riemannian manifolds

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