Stein neighborhood bases of embedded strongly pseudoconvex domains and approximation of mappings (Q950700)

The author constructs a Stein neighborhood basis for any compact subvariety \(A\) with strongly pseudoconvex boundary \(bA\) and Stein interior \(A\setminus bA\) in a complex space \(X\). This is an extension of a theorem due to \textit{Y.-T. Siu} [Invent. Math. 38, 89--100 (1976; Zbl 0343.32014)]. In the case \(A\) is a complex curve, the result coincides with the one proved by \textit{B. Drinovec Drnovšek} and \textit{F. Forstnerič} [Duke Math. J. 139, No. 2, 203--253 (2007; Zbl 1133.32002)]. The proof is an adaptation of their proof to the higher-dimensional case and uses ideas of \textit{J.-P. Demailly's} proof of Siu's theorem [Math. Z. 204, No. 2, 283--295 (1990; Zbl 0682.32017)]. For embedded stronlgy pseudoconvex domains in a complex manifold, he finds a basis of tubular Stein neighborhoods. Then, he applies these results to the approximation of holomorphic mappings.