On thickening of holomorphic hulls and envelopes of holomorphy on Stein spaces

Abstract

On a normal Stein variety [Formula: see text], we study the thickening problem, i.e. the problem whether the assumption that a compact set [Formula: see text] is contained in the interior of another compact set, [Formula: see text] implies that the same inclusion holds for their holomorphic hulls. An affirmative answer is given for [Formula: see text] with isolated quotient singularities. On any Stein space [Formula: see text] with isolated singularities, we prove thickening for those hulls which have analytic structure at the singular points, obtaining a limitation for possible counter-examples. In dimension [Formula: see text], we finally relate the holomorphic hulls to analytic extension from parts of strictly pseudoconvex boundaries.