Lower order eigenvalues of Dirichlet Laplacian
Lower order eigenvalues of Dirichlet Laplacian
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DOI：
10.1007/s00229-007-0136-9
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发表时间：
2008-02
影响因子：
0.6
通讯作者：
He-Jun Sun;Q. Cheng;Hongcang Yang
中科院分区：
文献类型：
--
作者：
He-Jun Sun;Q. Cheng;Hongcang Yang
本文研究了n维紧致黎曼流形中区域上Dirichlet Laplacian的特征值问题。首先给出特征值的一个一般不等式。作为它的应用之一，我们研究了n维复射影空间中整环上、复射影空间中紧致复子流形上和单位球面上Laplacian的特征值.利用Gram-Schmidt的正交化（QR分解定理），构造了试探函数。利用这些试函数，得到了低阶特征值的估计。
In this paper, we investigate an eigenvalue problem for the Dirichlet Laplacian on a domain in ann-dimensional compact Riemannian manifold. First we give a general inequality for eigenvalues. As one of its applications, we study eigenvalues of the Laplacian on a domain in ann-dimensional complex projective space, on a compact complex submanifold in complex projective space and on the unit sphere. By making use of the orthogonalization of Gram–Schmidt (QR-factorization theorem), we construct trial functions. By means of these trial functions, estimates for lower order eigenvalues are obtained.