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Isoperimetric control of the Steklov spectrum
Auteur(s)
Date de parution
2011-6-21
In
J. Funct. Anal.
Vol.
5
No
261
De la page
1384
A la page
1399
Résumé
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 uniforml 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.
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.
Identifiants
Type de publication
journal article
