Quasiconformal Contactomorphisms and Polynomial Hulls with Convex Fibers

摘要: Consider the polynomial hull of a smoothly varying family strictly convex smooth domains fibered over unit circle. It is well-known that boundary foliated by graphs analytic discs. We prove this foliation smooth, and we show it induces complex flow contactomor- phisms. These mappings are quasiconformal in sense Kor´ anyi Reimann. A similar bound on their distortion holds as one-dimensional case holomorphic motions. The special when fibers rotations fixed domain C 2 studied details.