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Colbois, Bruno
Résultat de la recherche
Uniform stability of the Dirichlet spectrum for rough perturbations
2013-10-29, Colbois, Bruno, Girouard, Alexandre, Iversen, Mette
Involutive isometries, eigenvalue bounds and a spectral property of Clifford tori
2012-2-17, Colbois, Bruno, Savo, Alessandro
Large eigenvalues and concentration
2011-4-21, Colbois, Bruno, Savo, Alessandro
Bounding the eigenvalues of the Laplace-Beltrami operator on compact submanifolds
2010-1-21, Colbois, Bruno, Dryden, Emily B, El Soufi, Ahmad
We give upper bounds for the eigenvalues of the La-place-Beltrami operator of a compact m-dimensional submanifold M of R^{m+p}. Besides the dimension and the volume of the submanifold and the order of the eigenvalue, these bounds depend on either the maximal number of intersection points of M with a p-plane in a generic position (transverse to M), or an invariant which measures the concentration of the volume of M in R^{m+p}. These bounds are asymptotically optimal in the sense of the Weyl law. On the other hand, we show that even for hypersurfaces (i.e., when p=1), the first positive eigenvalue cannot be controlled only in terms of the volume, the dimension and (for m>2) the differential structure.
Isoperimetric control of the spectrum of a compact hypersurface
2013-10-2, Colbois, Bruno, El Soufi, Ahmad, Girouard, Alexandre
Hilbert domains that admit a quasi-isometric embedding into Euclidean space
2011-12-21, Colbois, Bruno, Verovic, Patrick
Hilbert geometry for convex polygonal domains
2011-1-21, Colbois, Bruno, Vernicos, Constantin, Verovic, Patrick
Eigenvalue control for a Finsler--Laplace operator
2013-5-1, Barthelmé, Thomas, Colbois, Bruno
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.
Eigenvalue estimate for the rough Laplacian on differential forms
2010-2-21, Colbois, Bruno, Maerten, Daniel
We study the spectrum of the rough Laplacian acting on differential forms on a compact Riemannian manifold (M,g). We first construct on M metrics of volume 1 whose spectrum is as large as desired. Then, provided that the Ricci curvature of g is bounded below, we relate the spectrum of the rough Laplacian on 1--forms to the spectrum of the Laplacian on functions, and derive some upper bound in agreement with the asymptotic Weyl law.