location:  Publications → journals → CJM
Abstract view

# Quasiconformal Contactomorphisms and Polynomial Hulls with Convex Fibers

Published:1999-10-01
Printed: Oct 1999
• Zoltán M. Balogh
• Christoph Leuenberger
 Format: HTML LaTeX MathJax PDF PostScript

## Abstract

Consider 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 Kor\'anyi 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 $\C^2$ is studied in details.
 MSC Classifications: 32E20 - Polynomial convexity 30C65 - Quasiconformal mappings in ${\bf R}^n$, other generalizations