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

Isoperimetric Bounds for Eigenvalues of the Wentzell-Laplace, the Laplacian and a biharmonic Steklov Problem