Stein Neighborhood Bases of Embedded Strongly Pseudoconvex Domains and Approximation of Mappings

Abstract

In this paper we construct a Stein neighborhood basis for any compact subvariety A with strongly pseudoconvex boundary bA and Stein interior A\bA in a complex space X. This is an extension of a well known theorem of Siu. When A is a complex curve, our result coincides with the result proved by Drinovec-Drnovsek and Forstneric. We shall adapt their proof to the higher dimensional case, using also some ideas of Demailly’s proof of Siu’s theorem. For embedded strongly pseudoconvex domain in a complex manifold we also find a basis of tubular Stein neighborhoods. These results are applied to the approximation problem for holomorphic mappings.