$p$-双调和算子的第一特征值的等周上界和 Reilly 型不等式

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.

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

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.