Natural extensions of holomorphic motions |
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Authors: | Zbigniew Slodkowski |
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Affiliation: | (1) Department of Mathematics, University of Illinois at Chicago, 851 South Morgan Street, 60607-7045 Chicago, IL |
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Abstract: | We consider an arbitrary real analytic family Xz,
, over the closed unit disc
, of real analytic plane Jordan curves Xz. Ifj
e
iθ
,e
iθ
∋ ∂D, is an arbitrary real-analytic family of orientation-reversing homeomorphisms of
fixingX
e
iθ
pointwise, we show that there is a unique holomorphic motion of
extending the given motion of Jordan curves and consistent with the given family of involutions. If these generalized reflections
are defined using the barycentric extension construction of Douady-Earle-Nag, then the resulting extension method for holomorphic
motions of X is natural, that is Moebius-invariant and continuous with respect to variation of the given motion of X0. |
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Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications 30F60 32F15 32D15 |
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