A general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces
| dc.creator | Nguyen, Viet-Anh | |
| dc.date | 2007-03-25 | |
| dc.date.accessioned | 2026-07-07T07:53:53Z | |
| dc.date.available | 2026-07-07T07:53:53Z | |
| dc.description | 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 $\hat{W}:=\left\lbrace(z,w)\in X\times Y:\ \widetildeω(z,A,X)+\widetildeω(w,B,Y)<1 \right\rbrace$ such that $\hat{f}=f$ on $W\cap \hat{W},$ where $\widetildeω(\cdot,A,X)$ (resp. $\widetildeω(\cdot,B,Y))$ 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. | |
| dc.identifier | https://arxiv.org/abs/math/0703736 | |
| dc.identifier | http://arxiv.org/abs/math/0703736 | |
| dc.identifier | Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), Vol IV (2005), 219--254 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126394 | |
| dc.subject | Complex Variables | |
| dc.subject | 32D15, 32D10 | |
| dc.title | A general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces | |
| dc.type | text |