Inequalities for eigenvalues of Laplacian on domains and compact complex hypersurfaces in complex projective spaces
-
- Cheng Qing-Ming
- Department of Mathematics, Faculty of Science and Engineering, Saga University
-
- Yang Hongcang
- Academy of Mathematics and Systematical Sciences
Search this article
Abstract
It is well known that the spectrum of Laplacian on a compact Riemannian manifold M is an important analytic invariant and has important geometric meanings. There are many mathematicians to investigate properties of the spectrum of Laplacian and to estimate the spectrum in term of the other geometric quantities of M. When M is a bounded domain in Euclidean spaces, a compact homogeneous Riemannian manifold, a bounded domain in the standard unit sphere or a compact minimal submanifold in the standard unit sphere, the estimates of the k+1-th eigenvalue were given by the first k eigenvalues (see [9], [12], [19], [20], [22], [23], [24] and [25]). In this paper, we shall consider the eigenvalue problem of the Laplacian on compact Riemannian manifolds. First of all, we shall give a general inequality of eigenvalues. As its applications, we study the eigenvalue problem of the Laplacian on a bounded domain in the standard complex projective space CPn(4) and on a compact complex hypersurface without boundary in CPn(4). We shall give an explicit estimate of the k+1-th eigenvalue of Laplacian on such objects by its first k eigenvalues.
Journal
-
- Journal of the Mathematical Society of Japan
-
Journal of the Mathematical Society of Japan 58 (2), 545-561, 2006
The Mathematical Society of Japan
- Tweet
Details 詳細情報について
-
- CRID
- 1390282680093229696
-
- NII Article ID
- 10018381427
-
- NII Book ID
- AA0070177X
-
- ISSN
- 18811167
- 18812333
- 00255645
-
- MRID
- 2228572
-
- NDL BIB ID
- 7892161
-
- Text Lang
- en
-
- Data Source
-
- JaLC
- NDL
- Crossref
- CiNii Articles
- KAKEN
-
- Abstract License Flag
- Disallowed