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Regularity of varieties in strictly pseudoconvex domains. (English) Zbl 0737.32008
The author simplifies the proof of a boundary regularity theorem for purely \(p\)-dimensional subvarieties of strictly pseudo-convex domains that is contained in one of his previous papers [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 13, No. 1, 109-128 (1986; Zbl 0605.32011)]. As a corollary he obtains the following somewhat surprising result: Suppose \(\Omega\) is a bounded strictly pseudoconvex domain of class \(C^ 2\) in \(\mathbb{C}^ n\) with polynomially convex closure and \(M\) is a simple closed curve of class \(C^ 2\) contained in the boundary of \(\Omega\) that is complex tangential at least at one point; then \(M\) is polynomially convex.

32T99 Pseudoconvex domains
32E20 Polynomial convexity, rational convexity, meromorphic convexity in several complex variables
32C25 Analytic subsets and submanifolds
32H40 Boundary regularity of mappings in several complex variables
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