$p$-双调和算子的第一特征值的等周上界和 Reilly 型不等式

Isoperimetric Upper Bounds and Reilly-Type Inequalities for the First Eigenvalue of the $p$-Biharmonic Operator

中文关键词:  特征值  $p$-双调和算子  等周上界  Reilly-型不等式

英文关键词:eigenvalue  $p$-biharmonic operator  isoperimetric upper bounds  Reilly-type inequalities

中文摘要:

      在本文中,我们给出了嵌入到欧氏空间中的$n$维闭超曲面上$p$-双调和算子的第一特征值的一些等周上界.我们也给出了浸入到高维流形如欧氏空间,球面和射影空间中的闭子流形上$p$-双调和算子的第一特征值的一些Reilly-型不等式.

英文摘要:

      In this paper, we give some isoperimetric upper bounds for the first eigenvalue of the $p$-biharmonic operator of an $n$-dimensional embedded closed hypersurface in an Euclidean space. We also give Reilly-type inequalities for the first eigenvalue of the $p$-biharmonic operator of an $n$-dimensional closed submanifold immersed into a higher dimensional manifold such as an Euclidean space, a unit sphere, a projective space.