Isoperimetric upper bounds and Reilly-type inequalities for the first eigenvalue of the $p$-biharmonic operator

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

中文摘要:

      

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 embedded closed submanifold immersed into a higher dimensional manifold such as an Euclidean space, a unit sphere, a projective space.