Abstract

The author studies the question when for small \(r>0\) the set \(M^r:=\{z\in M: \|z\|<r\}\) is polynomially convex and, in the case where \(M^r\) is not polynomially convex, what is the structure of \(\widehat M^r\setminus M^r\). In particular, he shows that if \(M\) is contained in a strongly Levi flat hypersurface, then \(M\) is not locally polynomially convex at \(0\) and for small \(r>0\) the set \(\widehat M^r\setminus M^r\) is a foliation of disjoint analytic annuli.