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Boundary correspondence and dilatation of harmonic mappings

 

作者: Peter Duren,   Dmitry Khavinson,  

 

期刊: Complex Variables, Theory and Application: An International Journal  （Taylor Available online 1997）
卷期: Volume 33, issue 1-4  

页码: 105-111

 

ISSN:0278-1077

 

年代: 1997

 

DOI:10.1080/17476939708815015

 

出版商: Gordon and Breach Science Publishers

 

关键词: Harmonic mapping;Dilatation;Convex domain;Boundary correspondence;Quasiconformal mapping;Hopf's lemma;Primary 30C99;Secondary 31A05;Secondary 30C62

 

数据来源: Taylor

 

摘要:

If a sense-preserving harmonic mapping has dilatation of unit modulus on some boundary are, then it maps that are onto a concave are unless it is piecewise constant A theorem to this effect is proved with the aid of Hopf's lemma. A corollary is that if a harmonic mapping of the disk onto a convex domain extends to a “regular” homeomorphism of the closures, then it is quasiconformal.

 

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