The inner mapping radius of harmonic mappings of the unit disk
作者:
Michael Dorff,
Ted Suffridge,
期刊:
Complex Variables, Theory and Application: An International Journal
(Taylor Available online 1997)
卷期:
Volume 33,
issue 1-4
页码: 97-103
ISSN:0278-1077
年代: 1997
DOI:10.1080/17476939708815014
出版商: Gordon and Breach Science Publishers
关键词: Koebe theorem;mapping radius;harmonic mappings;30C20
数据来源: Taylor
摘要:
The classSnconsists of univalent, harmonic, and sense-preserving functionsJunit disk δ such thatwhere. Using a technique from Clinic and Shell-Small, we construct a family of I-slit mappings inSpby varying. AsW(z)changes, the tin of the slit slides along the negative real axis from the point U to - 1 In doing so. we establish that the inner mapping radiusp(f)can be as large as 4. In addition, we show that the inner mapping radius for functions incan be as small as 1/2 and as large as 2.
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