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Girouard, Alexandre
Résultat de la recherche
Uniform stability of the Dirichlet spectrum for rough perturbations
2013-10-29, Colbois, Bruno, Girouard, Alexandre, Iversen, Mette
Isoperimetric control of the spectrum of a compact hypersurface
2013-10-2, Colbois, Bruno, El Soufi, Ahmad, Girouard, Alexandre
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.