Generating all Ahlfors currents by a single entire curve

Yunling Chen; John Erik Fornæss; Song-Yan Xie

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arXiv · 2511.12473

Generating all Ahlfors currents by a single entire curve

Yunling Chen·John Erik Fornæss·Song-Yan Xie

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Abstract

Let $X$ be a compact complex manifold possessing the \emph{Runge approximation property on discs}, meaning that every holomorphic map from a closed disc into $X$ is approximable by a global holomorphic map from $\mathbb{C}$. We construct an entire curve $F : \mathbb{C} \to X$ such that the associated family of concentric holomorphic discs $\{F|_{\overline{\mathbb{D}}_r}\}_{r>0}$ generates all Ahlfors currents on $X$, thereby settling a conjecture of Sibony.

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Yunling Chen, John Erik Fornæss, Song-Yan Xie. 2025-11-16. Generating all Ahlfors currents by a single entire curve. https://arxiv.org/abs/2511.12473

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