紧致极小超曲面上两类特征值问题的等周不等式

ISOPERIMETRIC INEQUALITIES FOR TWO CLASSES OF EIGENVALUE PROBLEMS ON COMPACT MINIMAL HYPERSURFACES

在R^n的紧致极小超曲面上讨论了f-Laplician算子△_f和p-Laplician算子△_p的第一特征值问题.运用co-area公式分别得到了这两类算子第一特征值的等周不等式,以及等周不等式中等号成立的一个充要条件.

In this paper, we discuss the first eigenvalue problems of the f-Laplacian △f and p-Laplician △p on compact minimal hypersurfaces in R^n. Using a co-area formula, we obtain an isoperimetric inequality for the first eigenvalue of the f-Laplacian and p-Laplician respectively. Furthermore, we get a sufficient and necessary condition such that the equality in the isoperimetric inequality holds.