Mathematics – Complex Variables
Scientific paper
2007-03-25
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), Vol IV (2005), 219--254
Mathematics
Complex Variables
Scientific paper
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 $A$ (resp. $B$) be a non locally pluripolar subset of $X$ (resp. $Y$). We show that every separately holomorphic mapping $f: W:=(A\times Y) \cup (X\times B)\longrightarrow Z$ extends to a holomorphic mapping $\hat{f}$ on $\hat{W}:=\left\lbrace(z,w)\in X\times Y:\ \widetilde{\omega}(z,A,X)+\widetilde{\omega}(w,B,Y)<1 \right\rbrace$ such that $\hat{f}=f$ on $W\cap \hat{W},$ where $\widetilde{\omega}(\cdot,A,X)$ (resp. $\widetilde{\omega}(\cdot,B,Y))$ is the plurisubharmonic measure of $A$ (resp. $B$) relative to $X$ (resp. $Y$). Generalizations of this result for an $N$-fold cross are also given.
No associations
LandOfFree
A general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-703359