Abstract
In this paper we solve the \({\overline{\partial }}\)-problem along the leaves for two types of laminations: (i) Some open sets Ω of \({{\mathbb C}\times B}\) (where B is any differentiable manifold) endowed with the canonical foliation that is, the foliation whose leaves are the sections \({\Omega ^t=\{ z\in {\mathbb C}:(z,t)\in \Omega \}}\). We construct a solution to the equation \({\overline{\partial }h=fd\overline z}\) for any function \({f:\Omega\longrightarrow {\mathbb C}}\) of class \({C^{s}\,(s\in \mathbb{N}\cup\{ \infty \}),\,C^\infty}\) along the leaves and satisfies some growth conditions near the singularities. (ii) A complex lamination by Riemann surfaces obtained by suspending a homeomorphism of a closed set of the Euclidean space \({\mathbb{C}\times \mathbb{R}}\).
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Ben Charrada, R. Cohomology of Some Complex Laminations. Results. Math. 57, 33–41 (2010). https://doi.org/10.1007/s00025-009-0006-8
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DOI: https://doi.org/10.1007/s00025-009-0006-8