Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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 $\Omega _{1}$ and $\Omega _{2}$ be two domains in the complex plane with $\Omega _{1}\cap \Omega _{2}\not =\emptyset $. Suppose that $f_{j}:\Omega _{j}\to f_{j}(\Omega _{j})$ $(j=1,2)$ are two quasiconformal mappings satisfying $f_{1}\vert _{\Omega _{1}\cap \Omega _{2}} =f_{2}\vert _{\Omega _{1}\cap \Omega _{2}}$. Let $F$ be the mapping in $\Omega _{1}\cup \Omega _{2}$ defined by $F\vert _{\Omega _{j}}=f_{j}$ ($j=1,2$). If both $f_{1}$ and $f_{2}$ are uniquely extremal, is $F$ always uniquely extremal? It is shown in this paper that the answer to this problem is no.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30C75, 30C62

Retrieve articles in all journals with MSC (2000): 30C75, 30C62


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: http://dx.doi.org/10.1090/S0002-9939-04-07485-4
PII: S 0002-9939(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