On removability properties of ψ-uniform domains in Banach spaces

2012/06/01 by M. Huang, Huang, M., Матти Вуоринен +3
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1206.0128

openalex publication_date 2012/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that E denotes a real Banach space with the dimension at least 2. The main aim of this paper is to show that a domain D in E is a ψ-uniform domain if and only if D\backslash P is a ψ₁-uniform domain, and D is a uniform domain if and only if D\backslash P also is a uniform domain, whenever P is a closed countable subset of D satisfying a quasihyperbolic separation condition. This condition requires that the quasihyperbolic distance (w.r.t. D) between each pair of distinct points in P has a lower bound greater than or equal to (1)/(2).

Related

• On the subinvariance of uniform domains in Banach spaces
• On quasimöbius maps in real Banach spaces
• Quasimöbius invariance of uniform domains
• Characterizations of quasihyperbolic John domains and uniform domains in metric spaces
• On the subinvariance of uniform domains in metric spaces