Abstract:
In this paper, we prove that a family of holomorphic curves in $\mathbb{P}^N(\mathbb{C})$ that partially share moving as well as wandering hyperplanes with their derivatives is normal. By associating a moving hyperplane in $\mathbb{P}^1(\mathbb{C})$ to any holomorphic function, we also obtain a normality criterion for a family of meromorphic functions that partially share wandering holomorphic functions with their derivatives. Further, we devise a tractable representation of complex-valued holomorphic functions on a domain $D$ as functions from $D$ to $\mathbb{P}^2(\mathbb{C})$ to obtain a normality criterion that leads to a counterexample to the converse of Bloch's principle.
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