Loewner chains and evolution families on parallel slit half-planes
Loewner chains and evolution families on parallel slit half-planes
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DOI：
10.1016/j.jmaa.2023.127180
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发表时间：
2020-02
影响因子：
1.3
通讯作者：
Takuya Murayama
中科院分区：
文献类型：
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作者：
Takuya Murayama
本文定义并研究了复平面上多重连通域上的Loewner链及其演化族。这些链和族由平行狭缝半平面上的共形映射组成，分别具有一个和两个“时间”参数。通过类比的情况下，单连通域，我们开发了一个一般的理论Loewner链和多连通域上的发展家庭，特别是，证明他们服从弦Komatu-Loewner微分方程驱动的测度值过程。我们的方法涉及布朗运动与织补，做一些最近的研究。
In this paper, we define and study Loewner chains and evolution families on finitely multiply-connected domains in the complex plane. These chains and families consist of conformal mappings on parallel slit half-planes and have one and two “time” parameters, respectively. By analogy with the case of simply connected domains, we develop a general theory of Loewner chains and evolution families on multiply connected domains and, in particular, prove that they obey the chordal Komatu–Loewner differential equations driven by measure-valued processes. Our method involves Brownian motion with darning, as do some recent studies.