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Generalization of a theorem of Gonchar

Peter Pflug·Viet-Anh Nguyen
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Abstract

Let $X, Y$ be two complex manifolds, let $D\subset X,$ $ G\subset Y$ be two nonempty open sets, let $A$ (resp. $B$) be an open subset of $\partial D$ (resp. $\partial G$), and let $W$ be the 2-fold cross $((D\cup A)\times B)\cup (A\times(B\cup G)).$ Under a geometric condition on the boundary sets $A$ and $B,$ we show that every function locally bounded, separately continuous on $W,$ continuous on $A\times B,$ and separately holomorphic on $(A\times G) \cup (D\times B)$ "extends" to a function continuous on a "domain of holomorphy" $\hat{W}$ and holomorphic on the interior of $\hat{W}.$

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Peter Pflug, Viet-Anh Nguyen. 2006-10-11. Generalization of a theorem of Gonchar. https://doi.org/10.1007/s11512-006-0025-6

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