Cohomology of Some Complex Laminations

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 ${Omega ^t={ zin {mathbb C}:(z,t)in Omega }}$ . We construct a solution to the equation ${overline{partial }h=fdoverline z}$ for any function ${f:Omegalongrightarrow {mathbb C}}$ of class ${C^{s},(sin mathbb{N}cup{ infty }),,C^infty}$ 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 ${mathbb{C}times mathbb{R}}$ .