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Colbois, Bruno
Nom
Colbois, Bruno
Affiliation principale
Fonction
Professeur ordinaire
Email
Bruno.Colbois@unine.ch
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Curvature, Harnack's inequality, and a spectral characterization of nilmanifolds
2003, Aubry, Erwann, Colbois, Bruno, Ghanaat, Patrick, Ruh, Ernst
For closed n-dimensional Riemannian manifolds M with almost nonnegative Ricci curvature, the Laplacian on one-forms is known to admit at most n small eigenvalues. If there are n small eigenvalues, or if M is orientable and has n - 1 small eigenvalues, then M is diffeomorphic to a nilmanifold, and the metric is almost left invariant. We show that our results are optimal for n greater than or equal to 4.