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Quasiconformal Contactomorphisms and Polynomial Hulls with Convex Fibers

Published online by Cambridge University Press:  20 November 2018

Zoltán M. Balogh  and
Christoph Leuenberger
Zoltán M. Balogh
Affiliation:
Universität Bern, Mathematisches Institut, Sidlerstrasse 5, 3012 Bern, Schweiz email: zoltan@math-stat.unibe.ch
Christoph Leuenberger
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A. email: leuenb@math.purdue.edu
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Abstract

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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 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 ${{\text{C}}^{\text{2}}}$ is studied in details.

Keywords

32E2030C65
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 5 , 01 October 1999 , pp. 915 - 935
Copyright
Copyright © Canadian Mathematical Society 1999

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