The sharp estimates for the first eigenvalue of Paneitz operator on 4-dimensional submanifolds
arXiv:1010.3102
Abstract
In this note, we obtain the sharp estimates for the first eigenvalue of Paneitz operator for -dimensional compact submanifolds in Euclidean space. Since unit spheres and projective spaces can be canonically imbedded into Euclidean space, the corresponding estimates for the first eigenvalue are also obtained.