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Stein Neighborhood Bases of Embedded Strongly Pseudoconvex Domains and Approximation of Map**s

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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-Drnovšek and Forstnerič. 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 map**s.

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Authors and Affiliations

  1. Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

    Tadej Starčič

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  1. Tadej Starčič
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Correspondence to Tadej Starčič.

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Communicated by John Erik Fornaess.

Research supported by grants ARRS (3311-03-831049), Republic of Slovenia.

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Starčič, T. Stein Neighborhood Bases of Embedded Strongly Pseudoconvex Domains and Approximation of Map**s. J Geom Anal 18, 1133–1158 (2008). https://doi.org/10.1007/s12220-008-9037-8

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