Cover picture from Gunter Semmler, Math. Nachr. 284, No. 8-9, 1099-1117 (2011).The picture shows a cross section of a restriction manifold and two of its neighbourhoods. In the paper we prove that bounded analytic functions with boundary values in the closure of the domains surrounded by the restriction curves map inner points of the unit disc sufficiently close to the boundary to points in a given neighborhood of the cross section. The proof shows stepwise that inner points are not mapped to the discs covering the complement of the outer neighbourhood.
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