  In this paper, we prove some isoperimetric bounds for lower order eigenvalues
of the Wentzell-Laplace operator on bounded domains of a Euclidean space or a
Hadamard manifold, of the Laplacian on closed hypersurfaces of a Euclidean
space or a Hadamard manifold, and of a biharmonic Steklov problem on bounded
domains of a Euclidean space. Especially, interesting rigidity results can be
obtained if sharp bounds were achieved.
