Abstract
Let X and Y be two complex manifolds, let D⊂X and G⊂Y be two nonempty open sets, let A (resp. B) be an open subset of ∂D (resp. ∂G), and let W be the 2-fold cross ((D∪A)×B)∪(A×(B∪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×B, and separately holomorphic on (A×G)∪(D×B) “extends” to a function continuous on a “domain of holomorphy” \(\widehat{W}\) and holomorphic on the interior of \(\widehat{W}\).
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Pflug, P., Nguyên, VA. Generalization of a theorem of Gonchar. Ark Mat 45, 105–122 (2007). https://doi.org/10.1007/s11512-006-0025-6
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DOI: https://doi.org/10.1007/s11512-006-0025-6