Basic (Dolbeault) Cohomology of Foliated Manifolds with Boundary
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929242007142400 |
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| author | Ji, Qingchun Yao, Jun |
| author_facet | Ji, Qingchun Yao, Jun |
| contents | In this paper, we develop $L^2$ theory for Riemannian and Hermitian foliations on manifolds with basic boundary. We establish a decomposition theorem, various vanishing theorems, a twisted duality theorem for basic cohomologies and an extension theorem for basic forms of induced Riemannian foliation on the boundary. We prove the complex analogues for Hermitian foliations. To show the Dolbeault decomposition of basic forms, we extend Morrey's basic estimate to foliation version. We also investigate the global regularity for $\bar{\partial}_B$-equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08196 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Basic (Dolbeault) Cohomology of Foliated Manifolds with Boundary Ji, Qingchun Yao, Jun Differential Geometry Complex Variables In this paper, we develop $L^2$ theory for Riemannian and Hermitian foliations on manifolds with basic boundary. We establish a decomposition theorem, various vanishing theorems, a twisted duality theorem for basic cohomologies and an extension theorem for basic forms of induced Riemannian foliation on the boundary. We prove the complex analogues for Hermitian foliations. To show the Dolbeault decomposition of basic forms, we extend Morrey's basic estimate to foliation version. We also investigate the global regularity for $\bar{\partial}_B$-equations. |
| title | Basic (Dolbeault) Cohomology of Foliated Manifolds with Boundary |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2402.08196 |