数学年刊B辑（英文版）
數學年刊B輯（英文版）
수학년간B집（영문판）
CHINESE ANNALS OF MATHEMATICS,SERIES B
2012年
6期
823-830
,共8页
Yong Chan KIM%Toshiyuki SUGAWA
Yong Chan KIM%Toshiyuki SUGAWA
Yong Chan KIM%Toshiyuki SUGAWA
Univalent function%Holomorphic motion%Quasiconformal extension%Grunsky inequality%Univalence criterion
The authors mainly concern the set Uf of c ∈( C) such that the power deformationz(f(z/z))c is univalent in the unit disk |z| ＜ 1 for a given analytic univalent function f(z) =z + a2z2 +...in the unit disk.It is shown that Uf is a compact,polynomially convex subset of the complex plane (C) unless f is the identity function.In particular,the interior of Uf is simply connected.This fact enables us to apply various versions of the λ-lemma for the holomorphic family z(f(z)/z)c of injections parametrized over the interior of Uf.The necessary or sufficient conditions for Uf to contain 0 or 1 as an interior point are also given.
