Paneitz算子和p-Laplace算子的第一特征值的等周上界

Isoperimetric upper bounds for the first eigenvalue of the Paneitz operator and the p-Laplace operator

本文首先得到Euclid空间的n维嵌入闭超曲面上Paneitz算子的第一非零特征值的由Q曲率和平均曲率给出的一个最优估计,由此可得到一个等周上界.此外,本文还给出Euclid空间的n维嵌入闭超曲面上p-Laplace算子的第一非零特征值的一个等周上界.

In this paper, we give some sharp estimates for the first non-zero eigenvalue of Paneitz operators of an n-dimensional embedded closed hypersurface in a Euclidean space in terms of the mean curvature and the Q-curvature. Furthermore, we also give some isoperimetric upper bounds for the first non-zero eigenvalue of the p-Laplace operator of an n-dimensional embedded closed hypersurface in a Euclidean space.