Tangential Loewner hulls

Abstract

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.