Inequalities for eigenvalues of Laplacian on domains and compact complex hypersurfaces in complex projective spaces

By Qing Cheng, Hongcang Yang. 2006

51 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bad3c34798efcc1d8db2fb78b2c2222ce4817728

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In Applied Mathematics

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

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. P. Sicbaldi

In Mathematical Physics

1. Qing Cheng
2. Hongcang Yang
3. Ahmad El Soufi
4. S. Ilias
5. C. Xia
6. Evans M. Harrell II
7. R. Petrides

Citations in the corpus

• Universal inequalities for the eigenvalues of Laplace and Schr (2007, result): “In particular, the recent results of Cheng and Yang [8] and [9] concerning the eigenvalues of the Laplacian on - a domain or a minimal submanifold of S - a domain or a complex hypersurface of CP respectively, appear as particular cases of Theorem 3.”
• 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”
• Estimates for eigenvalues on Riemannian manifolds (2009, methodology): “By making use of the Rayleigh–Ritz inequality and the standard assertion on estimates for eigenvalues, we may have the following theorem which has been proved by Cheng and Yang [8]: Theorem CY.”
• Lower order eigenvalues of Dirichlet Laplacian (2008, unknown): “[9], [10], [11], [14], [15], [16], [17], [22], [23], [24], [27], [29], [30] and [31]).”
• Inequalities for eigenvalues of a clamped plate problem (2005, unknown): “[1–5,8–17,19–23,26,27,32–35,37], etc).”
• Extrinsic estimates for eigenvalues of the Laplace operator (2008, unknown): “More recently, Cheng and Yang [3], [ 5 ] have derived universal inequalities for eigenvalues of the Dirichlet eigenvalue problem of the Laplacian on a domain in a sphere or in a complex projective space.”
• 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.”