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arXiv · 2111.10680

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

Konstantinos Zarvalis
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Abstract

Let $Δ$ be a simply connected domain and $f:\mathbb{D} \to Δ$, where $\mathbb{D}$ is the unit disk, be a corresponding Riemann map. Let ${z_n}\subset Δ$ 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 $\partial \mathbb{D}$ by a certain angle $θ$ or by a certain set of angles $[θ_1, θ_2]$.

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Konstantinos Zarvalis. 2022-10-03. Characterizations of convergence by a given set of angles in simply connected domains. https://arxiv.org/abs/2111.10680

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