论文标题
Loewner连锁链和进化家庭在平行狭缝半套
Loewner chains and evolution families on parallel slit half-planes
论文作者
论文摘要
在本文中，我们在复杂平面中有限多重连接的域上定义和研究叶链链和进化家庭。这些链条和家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。通过与简单连接的域的情况类似，我们在乘以乘积域上开发了洛瓦纳链和进化族的一般理论，尤其是证明它们遵守了由度量值为值的过程驱动的弦弦komatu-loewner微分方程。我们的方法涉及布朗尼与瓦宁的运动，最近的一些研究也是如此。
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.
