Topology and bottom spectrum of transversally negatively curved foliations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911132370862080 |
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| author | Baudoin, Fabrice |
| author_facet | Baudoin, Fabrice |
| contents | We show that for any Riemannian foliation with a simply connected and negatively curved leaf space the normal exponential map of a leaf is a diffeomorphism. As an application, if the leaves are furthermore minimal submanifolds, we give a sharp estimate for the bottom of the spectrum of such a Riemannian manifold. Our proof of the spectral estimate also yields an estimate for the bottom of the spectrum of the horizontal Laplacian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topology and bottom spectrum of transversally negatively curved foliations Baudoin, Fabrice Differential Geometry Probability We show that for any Riemannian foliation with a simply connected and negatively curved leaf space the normal exponential map of a leaf is a diffeomorphism. As an application, if the leaves are furthermore minimal submanifolds, we give a sharp estimate for the bottom of the spectrum of such a Riemannian manifold. Our proof of the spectral estimate also yields an estimate for the bottom of the spectrum of the horizontal Laplacian. |
| title | Topology and bottom spectrum of transversally negatively curved foliations |
| topic | Differential Geometry Probability |
| url | https://arxiv.org/abs/2406.05503 |