Canonical models for a class of polynomially convex hulls

Abstract.

We use holomorphic motions and Beltrami equation to study a class of polynomially convex hulls in ℂ ² with Jordan fibers over the disc D. It is shown that every such hull is biholomorphically equivalent to a unique (up to suitable normalisation) canonical model. These models are the hulls whose complements in D×ℂmacr; are biholomorphic to a bidisc and are further characterized in terms of capacity of the fibers, Green’s function, pseudoconcavity and approximability by (very) special analytic polyhedra.