2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78481The ``complex Plateau problem'' (or boundary problem) in a complexe manifold X is the problem of characterizing the real submanifolds $Γ$ of X which are boundaries of analytic sub-varieties of $X \backslash Γ$. Our principal result treat the case $X=U\timesω$ where $U$ is a connected complex manifold and $ω$ is a disk-convex Kähler manifold. As a consequence, we obtain results of Harvey-Lawson, Dolbeault-Henkin and Dinh. We give generalizations of Hartogs-Levi and Hartogs-Bochner theorems. Finally, we prove that a strictly pseudo-convex CR structure embeddable in a compact Kähler manifold is embeddable in $\CC^n$ if and only if it has a non constant CR function.22 pagesComplex Variables32F25, 32F40, 32D15, 32C30text