On the subinvariance of uniform domains in Banach spaces

2012/09/20 by Manzi Huang, Xiantao Wang, Huang, Manzi +4
Mathematics · #30F45 #Analytic and geometric function theory #FOS: Mathematics #Holomorphic and Operator Theory #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations #Primary: 30C65 #Secondary: 30C20 #math.MG #msc:30C20 #msc:30C65 #msc:30F45

paper · pdf · doi:10.48550/arxiv.1209.4541

20 pages, 4 figures. arXiv admin note: text overlap with arXiv:1105.4684

openalex publication_date 2012/09/20 · arxiv created 2013/06/19 · arxiv updated 2013/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that E and E' denote real Banach spaces with dimension at least 2, that D⊂ E and D'⊂ 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(D₁) of every uniform subdomain D₁ in D under f is still uniform. This result answers an open problem of Väisälä in the affirmative.

Citations

• On quasimöbius maps in real Banach spaces

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