On weakly non-decreasable quasiconformal mappings

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:386

Article

Zhou Zemin²  Zhang Sihui¹  Chen Jixiu¹ 

[1] Fudan Univ, Dept Math, Shanghai 200433, Peoples R China

[2] Renmin Univ China, Dept Math, Beijing 100872, Peoples R China

关键词: Quasiconformal mapping;    Locally extremal;    Non-decreasable;    Weakly non-decreasable;    Teichmuller equivalence class;   

DOI  :  10.1016/j.jmaa.2011.08.040

来源: Elsevier

【 摘 要 】

The notion of non-decreasable dilatation for quasiconformal mappings, which was introduced by Edgar Reich, plays an important role in the theory of extremal quasiconformal mappings. It is an interesting open problem so far whether an extremal quasiconformal mapping with non-decreasable dilatation exists in every Teichmuller equivalence class. In this paper, we have partially solved this problem. It is proved that for every Teichmuller equivalence class [integral], there exists an extremal quasiconformal mapping g in [integral] with weakly non-decreasable dilatation. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free