Canonical models for a class of polynomially convex hulls (Q1359492)

Let \(D\) be the unit disc in \(\mathbb{C}\) and \(X\subset \partial D \times \mathbb{C}\) be a compact set in \(\mathbb{C}^2\) of the form \(X= \cup_{\zeta \in\partial D} \{\zeta\} \times X_\zeta\) with \(X_\zeta\) nonempty connected and simply connected in \(\mathbb{C}\). This paper deals with the polynomially convex hulls of \(X\). It is shown that these hulls are biholomorphic equivalent to a unique canonical model.