Generating all Ahlfors currents by a single entire curve
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912712526659584 |
|---|---|
| author | Chen, Yunling Fornæss, John Erik Xie, Song-Yan |
| author_facet | Chen, Yunling Fornæss, John Erik Xie, Song-Yan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12473 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generating all Ahlfors currents by a single entire curve Chen, Yunling Fornæss, John Erik Xie, Song-Yan Complex Variables 32A22, 32C30, 32Q56 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. |
| title | Generating all Ahlfors currents by a single entire curve |
| topic | Complex Variables 32A22, 32C30, 32Q56 |
| url | https://arxiv.org/abs/2511.12473 |