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Quasiconformal Contactomorphisms and Polynomial Hulls with Convex Fibers

Open Access article
 Printed: Oct 1999
  • Zoltán M. Balogh
  • Christoph Leuenberger
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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, 30C65 show english descriptions Polynomial convexity
Quasiconformal mappings in ${\bf R}^n$, other generalizations
32E20 - Polynomial convexity
30C65 - Quasiconformal mappings in ${\bf R}^n$, other generalizations

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