Sharp upper bounds are obtained for the first two nonzero Steklov eigenvalues in dimensions d >= 7 under volume-boundary normalization, derived from optimal weighted Neumann characterizations, plus strict bounds for higher eigenvalues on planar simply connected domains.
An Isoperimetric Inequality for the N-Dimensional Free Membrane Problem
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Geometric bounds for Steklov and weighted Neumann eigenvalues on Euclidean domains
Sharp upper bounds are obtained for the first two nonzero Steklov eigenvalues in dimensions d >= 7 under volume-boundary normalization, derived from optimal weighted Neumann characterizations, plus strict bounds for higher eigenvalues on planar simply connected domains.