Extensions of holomorphic motions to quasiconformal motions

2007 ◽  
pp. 199-208 ◽  
Author(s):  
Sudeb Mitra
Keyword(s):  
Holomorphic Motions

Holomorphic Motions and Teichmuller Spaces

1994 ◽  
Vol 343 (2) ◽  
pp. 927 ◽  
Author(s):  
C. J. Earle ◽  
I. Kra ◽  
S. L. Krushkal'
Keyword(s):  
Teichmüller Spaces ◽  
Holomorphic Motions ◽  
Teichmuller Spaces

Quasiconformal Contactomorphisms and Polynomial Hulls with Convex Fibers

1999 ◽  
Vol 51 (5) ◽  
pp. 915-935 ◽  
Author(s):  
Zoltán M. Balogh ◽  
Christoph Leuenberger
Keyword(s):  
Unit Circle ◽  
Complex Flow ◽  
One Dimensional ◽  
Holomorphic Motions ◽  
Strictly Convex ◽  
Fixed Domain ◽  
Polynomial Hulls ◽  
Polynomial Hull ◽  
The One ◽  
Special Case

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.

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