Local properties of quasihyperbolic and freely quasiconformal mappings

2011/10/28 by Yaxiang Li, Li, Yaxiang, Матти Вуоринен +3
Mathematics · #30C65 #30F45 (Primary) 30C20 (Secondary) #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1110.6269

openalex publication_date 2011/10/28 · 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 that if there exists some constant M>1 (resp. some homeomorphism ϕ) such that for all x∈ D, f: B(x,d_D(x))→ f(B(x,d_D(x))) is M-QH (resp. ϕ-FQC), then f is M₁-QH with M₁=M₁(M) (resp. ϕ₁-FQC with ϕ₁=ϕ₁(ϕ)). We apply our results to establish, in terms of the j_D metric, a sufficient condition for a homeomorphism to be FQC.

Related

• On quasimöbius maps in real Banach spaces
• On equicontinuity of homeomorphisms in a closure of a domain in metric spaces
• The radius of injectivity of local ring Q-homeomorphisms
• On behavior of homeomorphisms with inverse modulus conditions
• On the subinvariance of uniform domains in metric spaces