Estimates on Eigenvalues of Laplacian

By Qing Cheng, Hongcang Yang. 2005

125 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1c3dd3d21f64621d50dc14c86c42024d3b695c61

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In Applied Mathematics

1. Qing Cheng
2. Hongcang Yang
3. C. Xia
4. Ahmad El Soufi
5. S. Ilias
6. Qiaoling Wang
7. Evans M. Harrell II
8. Hong-wei Xu

In Computational Theory and Mathematics

1. Qing Cheng
2. Hongcang Yang
3. C. Xia
4. Hong-wei Xu
5. Ahmad El Soufi
6. S. Ilias
7. Evans M. Harrell II
8. Qiaoling Wang

Citations in the corpus

• Inequalities for eigenvalues of a clamped plate problem (2005, result): “where H0 = maxx∈� |H| and H is the mean curvature vector of M. When M is a unit n-sphere, the above inequality has also been obtained in [ 10 ].”
• Extrinsic estimates for eigenvalues of the Laplace operator (2008, unknown): “which is the Yang-type inequality for eigenvalues of the Dirichlet eigenvalue problem of Laplacian on a domain in a unit sphere obtained by Cheng and Yang [ 3 ].”
• Estimates for eigenvalues on Riemannian manifolds (2009, background): “For the Dirichlet eigenvalue problem of Laplacian on a domain in Sn(1), Cheng and Yang [6] have proved the following Yang-type inequality:”
• Bounds on eigenvalues of Dirichlet Laplacian (2006, result): “domain in an n-dimensional unit sphere, or an n-dimensional compact minimal submanifold in a unit sphere, or a bounded domain in an n-dimensional complex projective space, or an n-dimensional compact homogeneous Riemannian manifold, or a compact complex submanifold in an m-dimensional complex projec”
• Universal inequalities for the eigenvalues of Laplace and Schr (2007, background): “In the case of a minimally embedded submanifold of a sphere, Cheng and Yang state a bound on λk ([8], eq.”
• Isoperimetric Inequalities for Eigenvalues of the Laplacian (2007, result): “Thus far, Kröger [103, 104, 105] has obtained the most significant results towards a proof of Pólya’s conjecture for Neumann eigenvalues, (11.”
• Inequalities for eigenvalues of the drifting Laplacian on Riemannian manifolds (2014, background): “1 For some of the recent developments about universal inequalities for eigenvalues on Riemannian manifolds, we refer to [1–10,12–15,17,18,25–28] and the references therein.”
• Lower order eigenvalues of Dirichlet Laplacian (2008, unknown): “[8–10, 13–19, 22, 24, 25] and [26]).”