Propagation sets of holomorphic curves

Jian-Hua Zheng; Qiming Yan

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arXiv · 1912.03461

Propagation sets of holomorphic curves

Jian-Hua Zheng·Qiming Yan

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Abstract

We consider a problem of whether a property of holomorphic curves on a subset $X$ of the complex plane can be extended to the whole complex plane. In this paper, the property we consider is uniqueness of holomorphic curves. We introduce the propagation set. Simply speaking, $X$ is a propagation set if linear relation of holomorphic curves on the part of preimage of hyperplanes contained in $X$ can be extended to the whole complex plane. If the holomorphic curves are of infinite order, we prove the existence of a propagation set which is the union of a sequence of disks (In fact, the method applies to the case of finite order). For a general case, the union of a sequence of annuli will be a propagation set. The classic five-value theorem and four-value theorem of R. Nevanlinna are established in such propagation sets.

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BibTeX RIS

Jian-Hua Zheng, Qiming Yan. 2019-12-07. Propagation sets of holomorphic curves. https://arxiv.org/abs/1912.03461

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