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.