Abstract. We prove that every compact, pseudoconvex, orientable, CR manifold of C n , bounds a complex manifold in the C ∞ sense. In particular,∂ b has closed range. MSC: 32F10, 32F20, 32N15, 32T25

On a smooth domain Ω ⊂⊂ C n , we consider the Dirichlet problem for the complex Monge-Ampère equation ((dd c u) n = f dV, u| bΩ ≡ ϕ). We state the Hölder regularity of the solution u when the boundary value ϕ is Hölder continuous and the density f is only

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We give positive answer to a conjecture by Agranovsky. A continuous function on the sphere which has separate holomorphic extension along the complex lines which pass through three non aligned interior points, is the trace of a holomorphic function in the ball. MSC: 32F10, 32F20, 32N15, 32T25