Lower bounds for the spectral gap and an extension of the Bonnet-Myers theorem
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866910820412162048 |
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| author | Bonnefont, Michel Ouhabaz, El Maati |
| author_facet | Bonnefont, Michel Ouhabaz, El Maati |
| contents | 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 . |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_03542 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Lower bounds for the spectral gap and an extension of the Bonnet-Myers theorem Bonnefont, Michel Ouhabaz, El Maati Analysis of PDEs Functional Analysis Spectral Theory 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 . |
| title | Lower bounds for the spectral gap and an extension of the Bonnet-Myers theorem |
| topic | Analysis of PDEs Functional Analysis Spectral Theory |
| url | https://arxiv.org/abs/2112.03542 |