论文标题
Loewner痕迹的拓扑特征
Topological characterisations of Loewner traces
论文作者
论文摘要
（弦）Loewner微分方程通过连续实现的驱动功能编码半平面（又称痕迹）中的某些曲线。并非所有曲线都是痕迹；可以通过称为局部生长特性的几何条件来定义后者。在本文中，我们给出了另外两个表征迹线的等效条件：1。当且仅当映射任何初始段保留其连续性时，连续曲线是一个跟踪（可以看作是SLE的域Markov属性的类似物）。 2。（不一定简单的）迹线正是简单痕迹的统一限制。此外，使用Lind，Marshall，Rohde（2010）的方法，我们推断出痕迹的均匀收敛表示其驱动功能的均匀收敛性。
The (chordal) Loewner differential equation encodes certain curves in the half-plane (aka traces) by continuous real-valued driving functions. Not all curves are traces; the latter can be defined via a geometric condition called the local growth property. In this paper we give two other equivalent conditions that characterise traces: 1. A continuous curve is a trace if and only if mapping out any initial segment preserves its continuity (which can be seen as an analogue of the domain Markov property of SLE). 2. The (not necessarily simple) traces are exactly the uniform limits of simple traces. Moreover, using methods by Lind, Marshall, Rohde (2010), we infer that uniform convergence of traces imply uniform convergence of their driving functions.
