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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.

##### MSC:
 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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