Propagation sets of holomorphic curves
Propagation sets of holomorphic curves
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DOI：
10.1142/s0129167x20501268
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发表时间：
2019-12
影响因子：
0.6
通讯作者：
Jian-Hua Zheng;Qiming Yan
中科院分区：
文献类型：
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作者：
Jian-Hua Zheng;Qiming Yan
我们考虑复平面的子集上的全纯曲线的性质是否可以推广到整个复平面的问题。在本文中，我们考虑的性质是全纯曲线的唯一性。我们引入了传播集。简单来说，【公式：如果[公式：见正文]中包含的超平面的原像部分上的全纯曲线的线性关系可以推广到整个复平面，则[公式：见正文]是一个传播集。如果全纯曲线是无限级的，我们证明了一个传播集的存在性，它是一个序列的磁盘的联合。(In事实上，该方法适用于有限阶的情况。）在一般情况下，环序列的并集是一个传播集。经典的Nevanlinna五值定理和四值定理在这样的传播集上成立。
We consider a problem of whether a property of holomorphic curves on a subset [Formula: see text] of the complex plane can be extended to the whole complex plane. In this paper, the property we consider is the uniqueness of holomorphic curves. We introduce the propagation set. Simply speaking, [Formula: see text] is a propagation set if linear relation of holomorphic curves on the part of preimage of hyperplanes contained in [Formula: see text] 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 Nevanlinna are established in such propagation sets.