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.
Categories: math.CV