AbstractConsider the polynomial hull of a smoothly varying family of strictly convex smooth domains fibered over the unit circle. It is well-known that the boundary of the hull is foliated by graphs of analytic discs. We prove that this foliation is smooth, and we show that it induces a complex flow of contactomorphisms. These mappings are quasiconformal in the sense of Korányi and Reimann. A similar bound on their quasiconformal distortion holds as in the one-dimensional case of holomorphic motions. The special case when the fibers are rotations of a fixed domain in C2 is studied in details.
DIRECTIONAL DENSITY OF POLYNOMIAL HULLS AT SINGULARITIES
