Characterizations of convergence by a given set of angles in simply connected domains

2021/11/20 by Konstantinos Zarvalis, Zarvalis, Konstantinos
Mathematics · #30C35 #30D40 (Primary) 37F44 #31A15 (Secondary) #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2111.10680

openalex publication_date 2021/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Δ be a simply connected domain and f:\mathbbD → Δ, where \mathbbD is the unit disk, be a corresponding Riemann map. Let z_n⊂ Δ be a sequence with no accumulation points inside Δ. In the present article, we give necessary and sufficient conditions in terms of hyperbolic geometry which certify that f^-1(z_n) converges to a point of ∂ \mathbbD by a certain angle θ or by a certain set of angles [θ₁, θ₂].

Related

• A characterization of orthogonal convergence in simply connected domains
• Non-tangential limits and the slope of trajectories of holomorphic semigroups of the unit disc
• Boundary convergence and path divergence sets for bounded analytic\n functions in the disk
• On the hyperbolic metric of certain domains
• The Caratheodory Topology for Multiply Connected Domains I