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Girouard, Alexandre

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Girouard, Alexandre
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https://libra.unine.ch/handle/123456789/464

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    Isoperimetric control of the Steklov spectrum
    (2011-6-21)
    Colbois, Bruno 
    ;
    El Soufi, Ahmad
    ;
    Girouard, Alexandre 
    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.