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Colbois, Bruno
Nom
Colbois, Bruno
Affiliation principale
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Professeur ordinaire
Email
Bruno.Colbois@unine.ch
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Voici les éléments 1 - 6 sur 6
- PublicationMétadonnées seulementPetites valeurs propres des p-formes différentielles et classe d'Euler des S1-fibrés(2000-12-21)
; Courtois, GillesLet M(n, a, d) be the set of compact oriented Riemannian manifolds (M, g) of dimension n whose sectional curvature K-g and diameter d(g) satisfy \K-g\ less than or equal to a and d(g) less than or equal to d. Let M(n, a, d, rho) be the subset of M(n, a, d) of those manifolds (M, g) such that the injectivity radius is greater than or equal to rho. if (M, g) is an element of M(n + 1, a, d) and (N, h) is an element of M(n, a', d') are sufficiently close in the sense of Gromov-Hausdorff, M is a circle bundle over N according to a theorem of K. Fukaya. When the Gromov-Hausdorff distance between (M, g) and (N, h) is small enough, we show that there exists m(p) - b(p)(N) + b(p-1) (N) - b(p)(M) small eigenvalues of the Laplacian acting on differential p-forms on M, 1 < p < n + 1, where b(p) denotes the p-th Betti number. We give uniform bounds of these eigenvalues depending on the Euler class of the circle bundle S-1 --> M --> N and the Gromov-Hausdorff distance between (M, g) and (N, h). (C) 2000 Editions scientifiques et medicales Elsevier SAS. - PublicationMétadonnées seulementSur la multiplicité de la première valeur propre de l'opérateur de Schrödinger avec champ magnétique sur la sphère S2(1998)
; Courtois, GillesThe purpose of this text is to study the first eigenvalue of Schrodinger operator with magnetic field on the 2-sphere and to show that its multiplicity can be arbitrarily high. We also show that this multiplicity is bounded in terms of the curvature of the corresponding connection. This answers a question asked by Y. Colin de Verdiere. - PublicationMétadonnées seulementConvergence de variétés et convergence du spectre du Laplacien(1991-12-21)
; Courtois, Gilles - PublicationMétadonnées seulementA note on the 1st nonzero eigenvalue of the laplacian acting on p-forms(1990)
; Courtois, Gilles - PublicationMétadonnées seulement
- PublicationMétadonnées seulementLes valeurs propres inférieures à 1/4 des surfaces de Riemann de petit rayon d'injectivité(1989)
; Courtois, Gilles