Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590990 | Journal of Functional Analysis | 2011 | 16 Pages |
Abstract
We prove that the normalized Steklov eigenvalues of a bounded domain in a complete Riemannian manifold are bounded above in terms of the inverse of the isoperimetric ratio of the domain. Consequently, the normalized Steklov eigenvalues of a bounded domain in Euclidean space, hyperbolic space or a standard hemisphere are uniformly bounded above. On a compact surface with boundary, we obtain uniform bounds for the normalized Steklov eigenvalues in terms of the genus. We also establish a relationship between the Steklov eigenvalues of a domain and the eigenvalues of the Laplace–Beltrami operator on its boundary hypersurface.
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