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arXiv · 2402.08196

Basic (Dolbeault) Cohomology of Foliated Manifolds with Boundary

Qingchun Ji·Jun Yao
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Abstract

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.

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Qingchun Ji, Jun Yao. 2024-02-13. Basic (Dolbeault) Cohomology of Foliated Manifolds with Boundary. https://arxiv.org/abs/2402.08196

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