Holomorphic fiberings of pseudoconcave graphs. (Q1432520)

In the paper the following theorem is proved: Let \(\Gamma\subset \mathbb{C}^{n+1}\) be the graph of a continuous real function over a convex domain \(D\subset \mathbb{C}^n_2\times \mathbb{R}_u\) \((z= u+ iv)\) such that both components of the set \((D\times \mathbb{R}_v)\setminus\Gamma\) are pseudoconvex. Then, \(\Gamma= \bigcup A_\alpha\) is the union of pairwise disjoint holomorphic graphs \(A_\alpha: w= f_\alpha(z)\) over the corresponding domains \(G_\alpha\subset \mathbb{C}^n_z\); moreover, all \(A_\alpha\) are closed in \(\Gamma\), and all \(G_\alpha\) are contractible domains of holomorphy.