Regularity of varieties in strictly pseudoconvex domains. (English) Zbl 0737.32008

Forstnerič, Franc

Publ. Mat., Barc. 32, No. 1, 145-150 (1988).

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

Keywords:

boundary regularity; complex subvarieties of strictly pseudo-convex domains; polynomially convex