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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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