2005/03/16 by Peter Pflug, Pflug, Peter, Viêt‐Anh Nguyên +2
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Holomorphic and Operator Theory #math.CV #msc:32D10 #msc:32D15
paper · pdf · doi:10.48550/arxiv.math/0503326
43 pages, to appear in "Annales Polonici Mathematici". This is the revised version of our article put on Arxiv in March 2005
arxiv created 2006/10/29 · arxiv updated 2009/12/01
Let X, Y be two complex manifolds of dimension 1 which are countable at infinity, let D⊂ X, G⊂ Y be two open sets, let A (resp. B) be a subset of ∂ D (resp. ∂ G), and let W be the 2-fold cross ((D∪ A)× B)∪ (A×(B∪ G)). Suppose in addition that D (resp. G) is \it Jordan-curve-like on A (resp. B) and that A and B are \it of positive length. We determine the "envelope of holomorphy" W of W in the sense that any function locally bounded on W, measurable on A× B, and separately holomorphic on (A× G) ∪ (D× B) "extends" to a function holomorphic on the interior of W.