Abstract

Using recent development in Poletsky theory of discs, we prove the following result: Let $X,$ $Y$ be two complex manifolds, let $Z$ be a complex analytic space which possesses the Hartogs extension property, let $A$ be a non locally pluripolar subset of $X$. We show that every separately holomorphic mapping $f:\ W:= \cup \rightarrow Z$ extends to a holomorphic mapping $\hat{f}$ on $\widehat{W}:=\left\lbrace \in X\times Y:\ \widetilde{\omega }+\widetilde{\omega }<1 \right\rbrace $ such that $\hat{f}=f$ on $W\cap \widehat{W},$ where $\widetilde{\omega }$ )$ is the plurisubharmonic measure of $A$ relative to $X$. Generalizations of this result for an $N$-fold cross are also given