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

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It is well known that the spectrum of Laplacian on a compact Riemannian manifold <i>M</i> 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 <i>M</i>. When <i>M</i> 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 <i>k</i>+1-th eigenvalue were given by the first <i>k</i> eigenvalues (see [<b>9</b>], [<b>12</b>], [<b>19</b>], [<b>20</b>], [<b>22</b>], [<b>23</b>], [<b>24</b>] and [<b>25</b>]). 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 <b><i>CP</i></b><sup><i>n</i></sup>(4) and on a compact complex hypersurface without boundary in <b><i>CP</i></b><sup><i>n</i></sup>(4). We shall give an explicit estimate of the <i>k</i>+1-th eigenvalue of Laplacian on such objects by its first <i>k</i> eigenvalues.

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  • Journal of the Mathematical Society of Japan  

    Journal of the Mathematical Society of Japan 58(2), 545-561, 2006-04-01 

    The Mathematical Society of Japan

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各種コード

  • NII論文ID(NAID)
    10018381427
  • NII書誌ID(NCID)
    AA0070177X
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    00255645
  • NDL 記事登録ID
    7892161
  • NDL 雑誌分類
    ZM31(科学技術--数学)
  • NDL 請求記号
    Z53-A209
  • データ提供元
    CJP書誌  CJP引用  NDL  J-STAGE 
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