切向Loewner壳

摘要：

通过Loewner方程，实值驱动函数生成称为Loewner壳的集合。我们分析的驱动函数，接近0至少一样快$a (T-t)^r$ $t \to T$，其中$r \in (0, 1/2)$，并显示相应的Loewner壳在时间$T$的切线行为。我们还证明了一个关于迹存在的结果，并应用它说明了由$a(T-t)^r$驱动的$r \in (0,1/2)$的Loewner壳具有切迹曲线。

英文摘要：

Through the Loewner equation, real-valued driving functions generate sets called Loewner hulls. We analyze driving functions that approach 0 at least as fast as $a (T-t)^r$ as $t \to T$, where $r \in (0, 1/2)$, and show that the corresponding Loewner hulls have tangential behavior at time $T$. We also prove a result about trace existence and apply it to show that the Loewner hulls driven by $a(T-t)^r$ for $r \in (0,1/2)$ have a tangential trace curve.

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