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Polynomially convex hulls with piecewise smooth boundaries. (English) Zbl 0585.32016
We prove that for certain class of two-dimensional, smoothly embedded, totally real submanifolds M of \({\mathbb{C}}^ 2\) the polynomially convex hull \(\hat M\) of M is the union of images of smoothly embedded analytic disks in \({\mathbb{C}}^ 2\) with boundaries in M. The boundary of \(\hat M\) is piecewise smooth and is foliated by such disks. Our proof is based on a result of H. Alexander and J. Wermer [Math. Ann. 271, 99-109 (1985; Zbl 0538.32011)) and Slodkowski (to appear) who proved, in a slightly more general setting, that \(\hat M\) is the union of images of bounded analytic disks.

32E20 Polynomial convexity, rational convexity, meromorphic convexity in several complex variables
32V40 Real submanifolds in complex manifolds
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