In this paper, we discuss the first eigenvalue problemsof the -Laplacian and -Laplician on compact minimal hypersurfaces in . Using a co-area formula, we obtain an isoperimetric inequality for the first eigenvalue of the -Laplacian and -Laplician respectively.
Furthermore, we get a sufficient and necessary condition such that the equality in the isoperimetric inequality holds.
DENG Yihua.
ISOPERIMETRIC INEQUALITIES FOR TWO CLASSES OF EIGENVALUE PROBLEMS ON COMPACT MINIMAL HYPERSURFACES. Journal of Systems Science and Mathematical Sciences, 2013, 33(11): 1355-1362 https://doi.org/10.12341/jssms12211