Lower bounds for the spectral gap and an extension of the Bonnet-Myers theorem

Michel Bonnefont; El Maati Ouhabaz

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arXiv · 2112.03542

Lower bounds for the spectral gap and an extension of the Bonnet-Myers theorem

Michel Bonnefont·El Maati Ouhabaz

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Abstract

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 .

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Michel Bonnefont, El Maati Ouhabaz. 2021-12-07. Lower bounds for the spectral gap and an extension of the Bonnet-Myers theorem. https://arxiv.org/abs/2112.03542

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