Polynomially convex hulls with piecewise smooth boundaries (Q1071137)

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 \textit{H. Alexander} and \textit{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.