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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.

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