On univalence of the power deformation z(f(z)/z)(c)

Title
On univalence of the power deformation z(f(z)/z)(c)
Author(s)
김용찬Toshiyuki Sugawa[Toshiyuki Sugawa]
Issue Date
201211
Publisher
SHANGHAI SCIENTIFIC TECHNOLOGY LITERATURE PUBLISHING HOUSE
Citation
CHINESE ANNALS OF MATHEMATICS SERIES B, v.33, no.6, pp.823 - 830
Abstract
The authors mainly concern the set U (f) of c a a", such that the power deformation is univalent in the unit disk |z| < 1 for a given analytic univalent function f(z) = z + a (2) z (2) + aEuro broken vertical bar in the unit disk. It is shown that U (f) is a compact, polynomially convex subset of the complex plane a", unless f is the identity function. In particular, the interior of U (f) is simply connected. This fact enables us to apply various versions of the lambda-lemma for the holomorphic family of injections parametrized over the interior of U (f) . The necessary or sufficient conditions for U (f) to contain 0 or 1 as an interior point are also given.
URI
http://hdl.handle.net/YU.REPOSITORY/26966http://dx.doi.org/10.1007/s11401-012-0750-z
ISSN
0252-9599
Appears in Collections:
사범대학 > 수학교육과 > Articles
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