Estimates of the gaps between consecutive eigenvalues of Laplacian

Daguang Chen; Tao Zheng; Hongcang Yang

doi:10.2140/pjm.2016.282.293

Estimates of the gaps between consecutive eigenvalues of Laplacian

Daguang Chen, Tao Zheng, Hongcang Yang

School of Mathematics and Statistics

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

9 Citations (Scopus)

Abstract

For the eigenvalue problem of the Dirichlet Laplacian on a bounded domain in Euclidean space Rⁿ, we obtain estimates for the upper bounds of the gapsbetween consecutive eigenvalues which are the best possible in terms of the orders of the eigenvalues. Therefore, it is reasonable to conjecture that this type of estimate also holds for the eigenvalue problem on a Riemannian manifold. We give some particular examples.

Original language	English
Pages (from-to)	293-311
Number of pages	19
Journal	Pacific Journal of Mathematics
Volume	282
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2016.282.293
Publication status	Published - 1 Jun 2016

Keywords

Consecutive eigenvalues
Hyperbolic space
Laplacian
Riemannian manifold
Test function

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Chen, D., Zheng, T., & Yang, H. (2016). Estimates of the gaps between consecutive eigenvalues of Laplacian. Pacific Journal of Mathematics, 282(2), 293-311. https://doi.org/10.2140/pjm.2016.282.293

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KW - Test function

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Estimates of the gaps between consecutive eigenvalues of Laplacian

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Keywords

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