An extremal problem of quasiconformal mappings

Authors:
Zhong Li, Shengjian Wu and Zemin Zhou

Journal:
Proc. Amer. Math. Soc. **132** (2004), 3283-3288

MSC (2000):
Primary 30C75, 30C62

Published electronically:
April 21, 2004

MathSciNet review:
2073303

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, the following problem is studied. Let and be two domains in the complex plane with . Suppose that are two quasiconformal mappings satisfying . Let be the mapping in defined by (). If both and are uniquely extremal, is always uniquely extremal? It is shown in this paper that the answer to this problem is no.

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Additional Information

**Zhong Li**

Affiliation:
School of Mathematical Sciences, LMAM, Peking University, Beijing 100871, People’s Republic of China

Email:
lizhong@math.pku.edu.cn

**Shengjian Wu**

Affiliation:
School of Mathematical Sciences, LMAM, Peking University, Beijing 100871, People’s Republic of China

Email:
wusj@math.pku.edu.cn

**Zemin Zhou**

Affiliation:
School of Mathematical Sciences, LMAM, Peking University, Beijing 100871, People’s Republic of China

Email:
zeminzhou2000@163.com

DOI:
https://doi.org/10.1090/S0002-9939-04-07485-4

Received by editor(s):
December 3, 2002

Received by editor(s) in revised form:
July 15, 2003

Published electronically:
April 21, 2004

Additional Notes:
The first author was supported by the 973-Project Foundation of China (Grant TG199075105) and the second author was supported by the NNSF of China (Grants 10171003 and 10231040)

Communicated by:
Juha M. Heinonen

Article copyright:
© Copyright 2004
American Mathematical Society