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Search: MSC category 30C65 ( Quasiconformal mappings in ${\bf R}^n$, other generalizations )

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1. CJM 1999 (vol 51 pp. 915)

Balogh, Zoltán M.; Leuenberger, Christoph
Quasiconformal Contactomorphisms and Polynomial Hulls with Convex Fibers
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.

Categories:32E20, 30C65

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