Search

The ``complex Plateau problem'' (or boundary problem) in a complexe manifold X is the problem of characterizing the real submanifolds $\Gamma$ of X which are boundaries of analytic sub-varieties of $X \backslash \Gamma$. Our principal result treat the case $X=U\times\omega$ where $U$ is a connected complex manifold and $\omega$ is a disk-convex K\"ahler 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 K\"ahler manifold is embeddable in $\CC^n$ if and only if it has a non constant CR function., Comment: 22 pages

We give a wedge removability theorem for metrically thin sets of two codimensional Hausdorff null measure. This removability theorem combined with the wedge removability theorem of Merker for closed subsets of two codimensional manifolds, gives a CR-meromorphic extension theorem in the greater codimensional case., Comment: 13 pages