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

DOI Web Site 被引用文献5件 参考文献38件 オープンアクセス

書誌事項

公開日
2006
資源種別
journal article
DOI
  • 10.2969/jmsj/1149166788
公開者
一般社団法人 日本数学会

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説明

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.

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