BONNEFONT, Michel; OUHABAZ, El Maati

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BONNEFONT, Michel

OUHABAZ, El Maati
Institut de Mathématiques de Bordeaux [IMB]

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On a fairly general class of Riemannian manifolds M, we prove lower estimates in terms of the Ricci curvature for the spectral bound (when M has infinite volume) and for the spectral gap (when M has finite volume) for the Laplace-Beltrami operator. As a byproduct of our results we obtain an extension of the Bonnet-Myers theorem on the compactness of the manifold. We also prove lower bounds for the spectral gap for Ornstein-Uhlenbeck type operators on weighted manifolds. As an application we prove lower bounds for the spectral gap of perturbations of some radial measures on R n .< Réduire

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Schrödinger operators

Hodge-de Rham Laplacians

the spectral bound

the spectral gap

Ornstein-Uhlenbeck type operators

perturbations of radial measures. Contents

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LOWER BOUNDS FOR THE SPECTRAL GAP AND AN EXTENSION OF THE BONNET-MYERS THEOREM

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Résumé en anglais

Mots clés en anglais

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