A general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces

dc.creatorNguyen, Viet-Anh
dc.date2007-03-25
dc.date.accessioned2026-07-07T07:53:53Z
dc.date.available2026-07-07T07:53:53Z
dc.descriptionUsing 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.identifierhttps://arxiv.org/abs/math/0703736
dc.identifierhttp://arxiv.org/abs/math/0703736
dc.identifierAnn. Scuola Norm. Sup. Pisa Cl. Sci. (5), Vol IV (2005), 219--254
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126394
dc.subjectComplex Variables
dc.subject32D15, 32D10
dc.titleA general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces
dc.typetext

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