Quasiconformal Contactomorphisms and Polynomial Hulls with Convex Fibers
1999 ◽
Vol 51
(5)
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pp. 915-935
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Keyword(s):
The One
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AbstractConsider 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 C2 is studied in details.
Keyword(s):
1995 ◽
Vol 06
(06)
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pp. 805-823
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1983 ◽
Vol 24
(4)
◽
pp. 392-416
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1995 ◽
Vol 52
(1)
◽
pp. 97-105
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Keyword(s):