On the subinvariance of uniform domains in Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:407

Article

Huang, M.¹  Vuorinen, M.²  Wang, X.¹ 

[1] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China

[2] Univ Turku, Dept Math & Stat, Turku 20014, Finland

关键词: Uniform domain;    Quasiconformal mapping;    FQC mapping;    QH homeomorphism;    (c, h)-solid curve;   

DOI  :  10.1016/j.jmaa.2013.05.046

来源: Elsevier

【 摘 要 】

Suppose that E and E' denote real Banach spaces with dimension at least 2, that D subset of E and D' subset of E' are domains, and that f : D -> D' is a homeomorphism. In this paper, we prove the following subinvariance property for the class of uniform domains: suppose that f is a freely quasiconformal mapping and that D' is uniform. Then the image f (D-1) of every uniform subdomain D-1 in D under f is still uniform. This result answers an open problem of Vaisala in the affirmative. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free