Estimates on Eigenvalues of Laplacian |
| |
Authors: | Email author" target="_blank">Qing-Ming?ChengEmail author Hongcang?Yang |
| |
Institution: | (1) Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502, Japan;(2) Academy of Mathematics and Systematical Sciences, CAS, Beijing, 100080, China |
| |
Abstract: | In this paper, we study eigenvalues of Laplacian on either a bounded connected domain in an n-dimensional unit sphere Sn(1), or a compact homogeneous Riemannian manifold, or an n-dimensional compact minimal submanifold in an N-dimensional unit sphere SN(1). We estimate the k+1-th eigenvalue by the first k eigenvalues. As a corollary, we obtain an estimate of difference between consecutive eigenvlaues. Our results are sharper than ones of P. C. Yang and Yau 25], Leung 19], Li 20] and Harrel II and Stubbe 12], respectively. From Weyl s asymptotical formula, we know that our estimates are optimal in the sense of the order of k for eigenvalues of Laplacian on a bounded connected domain in an n-dimensional unit sphere Sn(1).Mathematics Subject Classification (2000): 35P15, 58G25, 53C42Research was partially supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science.Research was partially Supported by SF of CAS, Chinese NSF and NSF of USA. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|